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In model predictive control (MPC), the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The main computational effort when solving the CFTOC problem using an active-set (AS) method is often spent on computing the search directions, which in MPC corresponds to solving unconstrained finite-time optimal control (UFTOC) problems. This is commonly performed using Riccati recursions or generic sparsity exploiting algorithms. In this paper, the focus is efficient search direction computations for AS type methods. The system of equations to be solved at each AS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance of AS-type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization between AS iterations in a structured way is presented. A numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying, instead of re-computing, the Riccati factorization. This speedup can be important for AS-type solvers used for linear, nonlinear, and hybrid MPC. [ABSTRACT FROM PUBLISHER]

Finding the optimal solution to the constrained l0 -norm minimization problems in the recovery of compressive sensed signals is an NP-hard problem and it usually requires intractable combinatorial searching operations for getting the global optimal solution, unless using other objective functions (e.g., the l1 norm or lp norm) for approximate solutions or using greedy search methods for locally optimal solutions (e.g., the orthogonal matching pursuit type algorithms). In this paper, a neurodynamic optimization method is proposed to solve the l0 -norm minimization problems for obtaining the global optimum using a recurrent neural network (RNN) model. For the RNN model, a group of modified Gaussian functions are constructed and their sum is taken as the objective function for approximating the l0 norm and for optimization. The constructed objective function sets up a convexity condition under which the neurodynamic system is guaranteed to obtain the globally convergent optimal solution. An adaptive adjustment scheme is developed for improving the performance of the optimization algorithm further. Extensive experiments are conducted to test the proposed approach in this paper and the output results validate the effectiveness of the new method. [ABSTRACT FROM PUBLISHER]

Purpose – The key control characteristics (KCCs) are very important to control dimensional quality of the final product. The purpose of this paper is to propose optimization algorithm and rules of design KCCs by optimizing KCCs of 2D and 3D workpieces based on equations and candidate locating points. Design/methodology/approach – This paper analyzes optimization process of 2D and 3D rectangle workpieces based on equations and candidate locating points by using fruit fly optimization algorithm (FOA). For decreasing variables of the algorithm, the improved fruit fly optimization algorithm (IFOA) is presented. Moreover, the Euclidean norm of inverse Jacobian is used as the objective function of optimizing KCCs by comparing different objective functions. Finally, a case of side frame assembly is presented to illustrate design and optimization of KCCs through IFOA, and results show that the method proposed in this paper is efficient and precise. Findings – The paper provides some reasonable conclusions for the design and optimization of KCCs. Originality/value – This paper designs and optimizes KCCs of fixtures and parts to improve dimensional quality of the final product. [ABSTRACT FROM AUTHOR]

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the computational task, instead of using a single centralized processor to obtain a “global solution” of the scenario problem (SP), we resort to multiple interconnected processors that are distributed among different nodes of a network to simultaneously solve the SP. Then, we propose a primal-dual subgradient algorithm and a random projection algorithm to distributedly solve the SP over undirected and directed graphs, respectively. Both algorithms are given in an explicit recursive form with simple iterations, which are especially suited for processors with limited computational capability. We show that, if the underlying graph is strongly connected, each node asymptotically computes a common optimal solution to the SP with a convergence rate $O(1/(\sum _{t=1}^k\zeta ^t))$ , where $\lbrace \zeta ^t\rbrace$ is a sequence of appropriately decreasing stepsizes. That is, the RCO is effectively solved in a distributed way. The relations with the existing literature on robust convex programs are thoroughly discussed and an example of robust system identification is included to validate the effectiveness of our distributed algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with a general class of distributed constrained optimization problems over a multiagent network, where the global objective function is represented by the sum of all local objective functions. Each agent in the network only knows its own local objective function, and is restricted to a global nonempty closed convex set. We discuss the scenario where the communication of the whole multiagent network is expressed as a sequence of time-varying general unbalanced directed graphs. The directed graphs are required to be uniformly jointly strongly connected and the weight matrices are only row-stochastic. To collaboratively deal with the optimization problems, existing distributed methods mostly require the communication graph to be fixed or balanced, which is impractical and hardly inevitable. In contrast, we propose a new distributed projection subgradient algorithm which is applicable to the time-varying general unbalanced directed graphs and does not need each agent to know its in-neighbors’ out-degree. When the objective functions are convex and Lipschitz continuous, it is proved that the proposed algorithm exactly converges to the optimal solution. Simulation results on a numerical experiment are shown to substantiate feasibility of the proposed algorithm and correctness of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of distributed control for network systems aiming to achieve optimal steady-state performance. Motivated by recent research on reengineering cyber-physical systems, such as power systems and the Internet, we propose a two-step control retrofit procedure. First, we reformulate the dynamical system as an optimization algorithm to solve a certain optimization problem. Second, we combine a predefined steady-state optimization problem and the reformulated problem to systematically (re)design the control. As a result, the system automatically tracks the optimal solution of the predefined steady-state optimization problem and the control scheme can be implemented in a distributed and closed-loop manner. In order to investigate how general this framework is, we establish necessary and sufficient conditions under which a linear dynamical system can be viewed as an optimization algorithm. These conditions are characterized using properties of system matrices and related linear matrix inequalities. A practical example of frequency control in power systems shows the effectiveness of the proposed framework. [ABSTRACT FROM PUBLISHER]

Several sparsity-constrained algorithms, such as orthogonal matching pursuit (OMP) or the Frank–Wolfe (FW) algorithm, with sparsity constraints work by iteratively selecting a novel atom to add to the current nonzero set of variables. This selection step is usually performed by computing the gradient and then by looking for the gradient component with maximal absolute entry. This step can be computationally expensive especially for large-scale and high-dimensional data. In this paper, we aim at accelerating these sparsity-constrained optimization algorithms by exploiting the key observation that, for these algorithms to work, one only needs the coordinate of the gradient’s top entry. Hence, we introduce algorithms based on greedy methods and randomization approaches that aim at cheaply estimating the gradient and its top entry. Another of our contribution is to cast the problem of finding the best gradient entry as a best-arm identification in a multiarmed bandit problem. Owing to this novel insight, we are able to provide a bandit-based algorithm that directly estimates the top entry in a very efficient way. Theoretical observations stating that the resulting inexact FW or OMP algorithms act, with high probability, similar to their exact versions are also given. We have carried out several experiments showing that the greedy deterministic and the bandit approaches we propose can achieve an acceleration of an order of magnitude while being as efficient as the exact gradient when used in algorithms, such as OMP, FW, or CoSaMP. [ABSTRACT FROM PUBLISHER]

The recent literature indicates that preserving global pairwise sample similarity is of great importance for feature selection and that many existing selection criteria essentially work in this way. In this paper, we argue that besides global pairwise sample similarity, the local geometric structure of data is also critical and that these two factors play different roles in different learning scenarios. In order to show this, we propose a global and local structure preservation framework for feature selection (GLSPFS) which integrates both global pairwise sample similarity and local geometric data structure to conduct feature selection. To demonstrate the generality of our framework, we employ methods that are well known in the literature to model the local geometric data structure and develop three specific GLSPFS-based feature selection algorithms. Also, we develop an efficient optimization algorithm with proven global convergence to solve the resulting feature selection problem. A comprehensive experimental study is then conducted in order to compare our feature selection algorithms with many state-of-the-art ones in supervised, unsupervised, and semisupervised learning scenarios. The result indicates that: 1) our framework consistently achieves statistically significant improvement in selection performance when compared with the currently used algorithms; 2) in supervised and semisupervised learning scenarios, preserving global pairwise similarity is more important than preserving local geometric data structure; 3) in the unsupervised scenario, preserving local geometric data structure becomes clearly more important; and 4) the best feature selection performance is always obtained when the two factors are appropriately integrated. In summary, this paper not only validates the advantages of the proposed GLSPFS framework but also gains more insight into the information to be preserved in different feature selection tasks. [ABSTRACT FROM AUTHOR]

Purpose – The change in the way of active power filters (APF) location can lead to overall cost reduction due to less number or less power of APFs required. The goal of this paper was to minimize the APF currents what is equivalent to solution with less apparent power of installed devices. The next step consists in development of new methods of APF optimal location. Design/methodology/approach – Some scripts integrating optimization and harmonic analysis methods in Matlab and PCFLO software environments have been developed in order to achieve the goal. Findings – Solution to the minimization problem determines the current spectrum of an APF connected to a selected system bus in accordance with some optimization strategies which among others enable minimization of THDV coefficients. Research limitations/implications – The APF control algorithm defined in the frequency domain and based on given current spectrum could lead to some problems with synchronization between APF instantaneous current and compensated current waveforms. Originality/value – There are many papers on APFs but usually systems in which an APF is connected near a nonlinear load are analyzed. Some attempts to solve the more complex problems of synchronized multipoint compensation have been already made but there is still no generally accepted and commonly used solution. [ABSTRACT FROM AUTHOR]

This note presents further results based on the recent paper [J. Liang, H. Chen, and J. Lam, “An improved criterion for controllability of Boolean control networks,” IEEE Trans. Autom. Control, vol. 62, no. 11, pp. 6012–6018, Nov. 2017]. After some optimizations, the conventional method can be more efficient than the method used in the above paper. We also propose an improved method via combining the well known Tarjan's algorithm and depth-first search technique for the controllability analysis of Boolean control networks (BCNs). As a result, the computational complexity will not exceed $O(N^2)$ with $N=2^n$ , where $n$ is the number of state-variables in a BCN. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to compute the distance to instability for linear time-invariant delay systems with multiple delays, subjected to combined uncertainties on the system matrices and the delay parameters. The method is able to fully exploit structure and possible interdependencies between the uncertainties affecting the coefficient matrices, the property that realistic perturbations are real valued, and the structure of the delay equation. The resulting algorithm relies on a characterization in terms of the pseudospectral abscissa and on techniques from optimization over manifolds of matrices. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion, which we term the directed infinite flow property, holds and the auxiliary states of agents are uniformly bounded away from zero infinitely often, we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states. Moreover, for a random sequence of graphs generated using a so-called time-varying $B$ -irreducible probability matrix, we establish convergence rates for the proposed push-sum algorithm. [ABSTRACT FROM AUTHOR]

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation-based dimensionality reduction method linear discriminant analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through \ell 2,1 -norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the \ell 2,p -norm regularized case, which is more likely to offer better sparsity when $0

This paper considers a class of stochastic source-seeking problems to drive a mobile robot to the minimizer of a source signal. Our approach is first analyzed in an obstacle-free scenario, where measurements of the signal at the robot location and information of a contact sensor are required. We extend our results to environments with obstacles under mild assumptions on the step size. Our approach builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithms to a ball whose size depends on the step size that contains the location of the source. The novelty relies in that we consider nondifferentiable convex functions, a fixed step size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov function theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in a two-dimensional scenarios. [ABSTRACT FROM AUTHOR]

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch–Kuhn–Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper considers the problem of a leader that seeks to optimally influence the opinions of agents in a directed network through connecting with a limited number of the agents (“direct followers”), possibly in the presence of a fixed competing leader. The settings involving a single leader and two competing leaders are unified into a general combinatoric optimization problem, for which two heuristic approaches are developed. The first approach is based on a convex relaxation scheme, possibly in combination with the $\ell _1$ -norm regularization technique, and the second is based on a greedy selection strategy. The main technical novelties of this work are in the establishment of supermodularity of the objective function and convexity of its continuous relaxation. The greedy approach is guaranteed to have a lower bound on the approximation ratio sharper than $(1-1/e)$ , while the convex approach can benefit from efficient (customized) numerical solvers to have practically comparable solutions possibly with faster computation times. The two approaches can be combined to provide improved results. In numerical examples, the approximation ratio can be made to reach ${\text{90}\%}$ or higher depending on the number of direct followers. [ABSTRACT FROM AUTHOR]

Single-layer feedforward networks (SLFNs) have been proven to be a universal approximator when all the parameters are allowed to be adjustable. It is widely used in classification and regression problems. The SLFN learning involves two tasks: determining network size and training the parameters. Most current algorithms could not be satisfactory to both sides. Some algorithms focused on construction and only tuned part of the parameters, which may not be able to achieve a compact network. Other gradient-based optimization algorithms focused on parameters tuning while the network size has to be preset by the user. Therefore, trial-and-error approach has to be used to search the optimal network size. Because results of each trial cannot be reused in another trial, it costs much computation. In this paper, a hybrid constructive (HC)algorithm is proposed for SLFN learning, which can train all the parameters and determine the network size simultaneously. At first, by combining Levenberg–Marquardt algorithm and least-square method, a hybrid algorithm is presented for training SLFN with fixed network size. Then,with the hybrid algorithm, an incremental constructive scheme is proposed. A new randomly initialized neuron is added each time when the training entrapped into local minima. Because the training continued on previous results after adding new neurons, the proposed HC algorithm works efficiently. Several practical problems were given for comparison with other popular algorithms. The experimental results demonstrated that the HC algorithm worked more efficiently than those optimization methods with trial and error, and could achieve much more compact SLFN than those construction algorithms. [ABSTRACT FROM PUBLISHER]

This paper proposes a distributed model predictive control (MPC) approach for a family of discrete-time linear systems with local (uncoupled) and global (coupled) constraints. The proposed approach is based on the dual problem of an overall MPC optimization problem involving all systems, which is then solved distributively using a modified distributed Nesterov-accelerated-gradient algorithm. To further reduce the computational requirement, this approach allows for early termination of the distributed gradient algorithm. This is made possible via a consensus algorithm that determines the satisfaction of the termination condition and by appropriate tightening of the coupled constraints. Under reasonable assumptions, the approach is able to produce a suboptimal solution as long as the network of the systems is connected while ensuring recursive feasibility and exponential stability of the closed-loop system. The performance of the proposed approach is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has recently become a very popular unsupervised learning method because of its representational properties of factors and simple multiplicative update algorithms for solving the NMF. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, the convergence of multiplicative update algorithms has not been well resolved. This paper first discusses the convergence of existing multiplicative update algorithms. We then propose a new multiplicative update algorithm for minimizing the Euclidean distance between approximate and true values. Based on the optimization principle and the auxiliary function method, we prove that our new algorithm not only converges to a stationary point, but also does faster than existing ones. To verify our theoretical results, the experiments on three data sets have been conducted by comparing our proposed algorithm with other existing methods. [ABSTRACT FROM AUTHOR]

This paper describes an efficient algorithm for designing lattice wave digital (LWD) filters (parallel connections of two all-pass filters) with short-coefficient wordlength. The coefficient optimization is performed using the following three steps. First, an initial infinite-precision filter is designed such that it exceeds the given criteria in order to provide some tolerance for co-efficient quantization. Second, a nonlinear optimization algorithm is used for determining a parameter space of the infinite-precision coefficients including the feasible space where the filter meets the given criteria. The third step involves finding the filter parameters in this space so that the resulting filter meets the given criteria with the simplest coefficient representation forms. The proposed algorithm guarantees that the optimum finite-precision solution can be found for both the fixed-point binary and multiplierless coefficient representation forms. In addition, this algorithm is applicable for producing the desired finite-precision solutions for both conventional and approximately linear-phase LWD filters. Comparisons with some other existing quantization schemes show that the proposed algorithm gives the best finite-precision solutions in all examples taken from the literature. [ABSTRACT FROM AUTHOR]

In this paper, the problem of maximizing power-system loadability with multiple complementarity constraints representing generator limits is examined. The structure of the loadability surface is investigated, the various type of limits are classified and a general algorithm to optimize settings of control variables, in order to maximize loadability margin is developed. The importance of nonsmooth corner points (CPs) of the loadability surface that are due to the simultaneous occurrence of several loadability conditions is discussed. At such limits, maximization, of loadability margin is performed based on techniques provided by nonlinear optimization theory. For this purpose an algorithm to identify multiple binding constraints on a CP is developed. Illustrative examples on small, but realistic systems are included. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stochastic model to describe how search service providers charge client companies based on users' queries for the keywords related to these companies' ads by using certain advertisement assignment strategies. We formulate an optimization problem to maximize the long-term average revenue for the service provider under each client's long-term average budget constraint and design an online algorithm which captures the stochastic properties of users' queries and click-through behaviors. We solve the optimization problem by making connections to scheduling problems in wireless networks, queueing theory and stochastic networks. Unlike prior models, we do not assume that the number of query arrivals is known. Due to the stochastic nature of the arrival process considered here, either temporary “free” service, i.e., service above the specified budget (which we call “overdraft”) or under-utilization of the budget (which we call “underdraft”) is unavoidable. We prove that our online algorithm can achieve a revenue that is within O(\epsilon) of the optimal revenue while ensuring that the overdraft or underdraft is O(1/\epsilon), where \epsilon can be arbitrarily small. With a view towards practice, we can show that one can always operate strictly under the budget. In addition, we extend our results to a click-through rate maximization model and also show how our algorithm can be modified to handle non-stationary query arrival processes and clients with short-term contracts. [ABSTRACT FROM AUTHOR]

Abstract: Digital watermarking is a useful solution for digital rights management systems, and it has been a popular research topic in the last decade. Most watermarking related literature focuses on how to resist deliberate attacks by applying benchmarks to watermarked media that assess the effectiveness of the watermarking algorithm. Only a few papers have concentrated on the error-resilient transmission of watermarked media. In this paper, we propose an innovative algorithm for vector quantization (VQ) based image watermarking, which is suitable for error-resilient transmission over noisy channels. By incorporating watermarking with multiple description coding (MDC), the scheme we propose to embed multiple watermarks can effectively overcome channel impairments while retaining the capability for copyright and ownership protection. In addition, we employ an optimization technique, called tabu search, to optimize both the watermarked image quality and the robustness of the extracted watermarks. We have obtained promising simulation results that demonstrate the utility and practicality of our algorithm. [Copyright &y& Elsevier]

We consider a setting where multiple vehicles form a team cooperating to visit multiple target points and collect rewards associated with them. The team objective is to maximize the total reward accumulated over a given time interval. Complicating factors include uncertainties regarding the locations of target points and the effectiveness of collecting rewards, differences among vehicle capabilities, and the fact that rewards are time-varying. We propose a receding horizon (RH) controller suitable for dynamic and uncertain environments, where combinatorially complex assignment algorithms are infeasible. The control scheme dynamically determines vehicle trajectories by solving a sequence of optimization problems over a planning horizon and executing them over a shorter action horizon. This centralized scheme can generate stationary trajectories in the sense that they guide vehicles to target points, even though the controller is not explicitly designed to perform any discrete point assignments. This paper establishes conditions under which this stationarity property holds in settings that are analytically tractable, quantifies the cooperative properties of the controller, and includes a number of illustrative simulation examples. [ABSTRACT FROM AUTHOR]

The Intelligent Water Drop (IWD) algorithm is a recent stochastic swarm-based method that is useful for solving combinatorial and function optimization problems. In this paper, we propose an IWD ensemble known as the Master-River, Multiple-Creek IWD (MRMC-IWD) model, which serves as an extension of the modified IWD algorithm. The MRMC-IWD model aims to improve the exploration capability of the modified IWD algorithm. It comprises a master river which cooperates with multiple independent creeks to undertake optimization problems based on the divide-and-conquer strategy. A technique to decompose the original problem into a number of sub-problems is first devised. Each sub-problem is then assigned to a creek, while the overall solution is handled by the master river. To empower the exploitation capability, a hybrid MRMC-IWD model is introduced. It integrates the iterative improvement local search method with the MRMC-IWD model to allow a local search to be conducted, therefore enhancing the quality of solutions provided by the master river. To evaluate the effectiveness of the proposed models, a series of experiments pertaining to two combinatorial problems, i.e., the travelling salesman problem (TSP) and rough set feature subset selection (RSFS), are conducted. The results indicate that the MRMC-IWD model can satisfactorily solve optimization problems using the divide-and-conquer strategy. By incorporating a local search method, the resulting hybrid MRMC-IWD model not only is able to balance exploration and exploitation, but also to enable convergence towards the optimal solutions, by employing a local search method. In all seven selected TSPLIB problems, the hybrid MRMC-IWD model achieves good results, with an average deviation of 0.021% from the best known optimal tour lengths. Compared with other state-of-the-art methods, the hybrid MRMC-IWD model produces the best results (i.e. the shortest and uniform reducts of 20 runs) for all13 selected RSFS problems. [ABSTRACT FROM AUTHOR]

Recently, krill herd algorithm (KHA) is proposed for the solution of global optimization problem. Various chaotic maps are considered in the proposed chaotic KHA (CKHA) of the present work to improve the performance of basic KHA method. It is observed that Logistic map based CKHA offers better results as compared other chaotic maps. The performance of the proposed CKHA is tested on standard 26-bus and IEEE 57-bus test power systems for the solution of optimal power flow of power system with different objectives that reflect minimization of fuel cost or active power loss or sum of total voltage deviation. Results obtained by using CKHA are compared to other evolutionary optimization techniques surfaced in the recent state-of-the-art literature. The results presented in this paper show that the proposed CKHA algorithm outperforms the other techniques in terms of convergence rate and global search ability. [ABSTRACT FROM AUTHOR]

Artificial immune system is a class of computational intelligence methods drawing inspiration from human immune system. As one type of popular artificial immune computing model, clonal selection algorithm (CSA) has been widely used for many optimization problems. CSA mainly generates new schemes by hyper-mutation operators which simulate the immune response process. However, these hyper-mutation operators, which usually perturb the antibodies in population, are semi-blind and not effective enough for complex optimization problems. In this paper, we propose a hybrid learning clonal selection algorithm (HLCSA) by incorporating two learning mechanisms, Baldwinian learning and orthogonal learning, into CSA to guide the immune response process. Specifically, (1) Baldwinian learning is used to direct the genotypic changes based on the Baldwin effect, and this operator can enhance the antibody information by employing other antibodies’ information to alter the search space; (2) Orthogonal learning operator is used to search the space defined by one antibody and its best Baldwinian learning vector. In HLCSA, the Baldwinian learning works for exploration (global search) while the orthogonal learning for exploitation (local refinement). Therefore, orthogonal learning can be viewed as the compensation for the search ability of Baldwinian learning. In order to validate the effectiveness of the proposed algorithm, a suite of sixteen benchmark test problems are fed into HLCSA. Experimental results show that HLCSA performs very well in solving most of the optimization problems. Therefore, HLCSA is an effective and robust algorithm for optimization. [ABSTRACT FROM AUTHOR]

We present a fast distributed solution to the convex network flow optimization problem. Our approach uses a family of dual descent algorithms that approximate the Newton direction to achieve faster convergence rates than existing distributed methods. The approximate Newton directions are obtained through matrix splitting techniques and sparse Taylor approximations of the inverse Hessian. We couple this descent direction with a distributed line search algorithm which requires the same information as our descent direction to compute. We show that, similarly to conventional Newton methods, the proposed algorithm exhibits super-linear convergence within a neighborhood of the optimal value. Numerical experiments corroborate that convergence times are between one to two orders of magnitude faster than existing distributed optimization methods. A connection with recent developments that use consensus to compute approximate Newton directions is also presented. [ABSTRACT FROM PUBLISHER]

Abstract: This paper presents a new technique for designing IIR filters that have minimum deviation from equiripple response. The algorithm is also able to find transfer functions with unequal numerator and denominator orders, which are suitable for both digital and analog IIR sampled-data realizations. Elliptic filters are produced as a particular case, when equal numerator and denominator orders are specified. Pole-zero mapping is used for scalar update of optimization parameters, thereby reducing the algorithm complexity. Zeros are structurally allocated on the unit circumference for efficient stopband shaping. Moreover, filter stability is easily enforced by restricting the radii of the poles to be lower than 1. A Taylor series expansion is employed to determine the step size of the parameter updates. The proposed approach is based on evaluations of partial cost functions to avoid local minima, and hence increase the robustness and the convergence rate of the optimization process. Design examples are shown to illustrate the efficacy of the proposed design technique, compared to alternative design techniques. [Copyright &y& Elsevier]

Abstract: This paper proposes an optimization-based method to design orthonormal wavelet filters with improved frequency separation. The proposed approach adopts a parameterization of orthogonal filter banks which ensures that the resulting wavelets have at least two vanishing moments. The filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to cut-off sharpness. In comparison with standard orthonormal filters, the proposed method is shown to provide better trade-off between frequency selectivity and time resolution. For illustration, the optimized filters are employed in an application example involving the use of a wavelet-packet system identification scheme. As a result, the identification errors are smaller than those obtained by using a non-optimized filter with the same length. [Copyright &y& Elsevier]

The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent coordination, estimation in sensor networks, and large-scale machine learning. We develop and analyze distributed algorithms based on dual subgradient averaging, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our analysis allows us to clearly separate the convergence of the optimization algorithm itself and the effects of communication dependent on the network structure. We show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network, and confirm this prediction's sharpness both by theoretical lower bounds and simulations for various networks. Our approach includes the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication. [ABSTRACT FROM AUTHOR]

Consider an agent who seeks to traverse the shortest path in a graph having random edge weights. If the agent has no side information about the realizations of the edge weights, it should simply take the path of least average length. We consider a generalization of this framework whereby the agent has access to a limited amount of side information about the edge weights ahead of choosing a path. We define a measure for information quantity, provide bounds on the agent's performance relative to the amount of side information it receives, and present algorithms for optimizing side information. The results are based on a new graph characterization tied to shortest path optimization. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces a novel optimization procedure for the design of group delay equalizers, which is simple to implement, robust and of fast convergence. A pole-zero placement technique is applied to ensure filter stability and direct updating equations. By cascading second-order allpass filter sections to the IIR filter to be equalized, the technique is able to produce group delay responses that are practically as close to a flat response as desired. The new optimization scheme is shown to avoid local minima often encountered by other algorithms used in the design of delay equalizers. Simulation results are presented to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: Work on single tone frequency estimation has focused on uniformly sampled data. However, it has been shown that, for a given number of samples, more information on the frequency of a signal can be gained by non-uniform sampling schemes [M. Wieler, S. Trittler, F.A. Hamprecht, Optimal design for single tone frequency estimation, Digital Signal Process., in press]. Unfortunately, an optimum sampling pattern (that, for example, minimizes the Cramér–Rao bound) does not automatically have a fast and simple algorithm for frequency estimation associated with it. For application in an interferometric measurement system, an algorithm is needed that gathers as much information as possible from a low number of samples, while at the same time keeping the computational effort sufficiently low to process millions of time series in a few seconds. This paper proposes a simple approximation to the optimum sampling pattern by using uniformly sampled blocks of data and further proposes to estimate phase and frequency in each of these blocks and to exploit these intermediate results in the final estimation. An approach to do so is investigated in detail. Results are compared to the Cramér–Rao bound (CRB), and it is shown that this algorithm almost reaches this limit on the variance of unbiased estimators, at a computational complexity lower than that of a typical FFT-based approach. For samples and a signal-to-noise ratio of 10, the standard deviation of the frequency estimate is lower by more than 50% compared to uniform sampling. In addition, the algorithm can easily be applied to poorly characterized systems, e.g. systems for which the noise is not known exactly. Finally, we demonstrate that the proposed strategy yields results that are within 3% of the theoretically achievable accuracy for the theoretically optimum sampling pattern. [Copyright &y& Elsevier]

Heuristic search techniques are highly flexible, though they represent computationally intensive optimization methods that may require thousands of evaluations of expensive objective functions. This paper integrates MODSIM, a generalized river basin network flow model, a particle swarm optimization (PSO) algorithm and artificial neural networks into a modeling framework for optimum water allocations at basin scale. MODSIM is called in the PSO model to simulate a river basin system operation and to evaluate the fitness of each set of selected design and operational variables with respect to the model's objective function, which is the minimization of the system's design and operational cost. Since the direct incorporation of MODSIM into a PSO algorithm is computationally prohibitive, an ANN model as a meta-model is trained to approximate the MODSIM modeling tool. The resulting model is used in the problem of optimal design and operation of the upstream Sirvan river basin in Iran as a case study. The computational efficiency of the model makes it possible to analyze the model performance through changing its parameters so that better solutions are obtained compared to those of the original PSO-MODSIM model. [ABSTRACT FROM AUTHOR]

Establishing the neighbor list to efficiently calculate the inter-atomic forces consumes the majority of computation time in molecular dynamics (MD) simulation. Several algorithms have been proposed to improve the computation efficiency for short-range interaction in recent years, although an optimized numerical algorithm has not been provided. Based on a rigorous definition of Verlet radius with respect to temperature and list-updating interval in MD simulation, this paper has successfully developed an estimation formula of the computation time for each MD algorithm calculation so as to find an optimized performance for each algorithm. With the formula proposed here, the best algorithm can be chosen based on different total number of atoms, system average density and system average temperature for the MD simulation. It has been shown that the Verlet Cell-linked List (VCL) algorithm is better than other algorithms for a system with a large number of atoms. Furthermore, a generalized VCL algorithm optimized with a list-updating interval and cell-dividing number is analyzed and has been verified to reduce the computation time by in a MD simulation for a two-dimensional lattice system. Due to similarity, the analysis in this study can be extended to other many-particle systems. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to propose the Human Evolutionary Model (HEM) as a novel computational method for solving search and optimization problems with single or multiple objectives. HEM is an intelligent evolutionary optimization method that uses consensus knowledge from experts with the aim of inferring the most suitable parameters to achieve the evolution in an intelligent way. HEM is able to handle experts’ knowledge disagreements by the use of a novel concept called Mediative Fuzzy Logic (MFL). The effectiveness of this computational method is demonstrated through several experiments that were performed using classical test functions as well as composite test functions. We are comparing our results against the results obtained with the Genetic Algorithm of the Matlab’s Toolbox, Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), Particle Swarm Optimizer (PSO), Cooperative PSO (CPSO), G3 model with PCX crossover (G3-PCX), Differential Evolution (DE), and Comprehensive Learning PSO (CLPSO). The results obtained using HEM outperforms the results obtained using the abovementioned optimization methods. [Copyright &y& Elsevier]

This paper presents a new method for optimizing continuous complex functions based on a learning automaton. This method can be considered as active learning permitting to select on-line the most significant data samples in order to quickly converge to a quasi global optimum of the functions to be optimized with a fewer number of tests or calculations. Like other stochastic optimization algorithms, it aims at finding a compromise between exploitation and exploration, i.e. converging to the nearest local optima and exploring the function behavior in order to discover global optimal regions. During the optimization procedure, this method enhances local search in interesting regions or intervals and reduces the whole searching space by removing useless regions or intervals. [ABSTRACT FROM AUTHOR]

This paper falls within the scope of studies concerning the optimization of the functioning of hydrothermal systems. We have developed a much simpler theory than previous ones that resolves the problem of minimization of a functionalF(z)=∫0TL(t,z(t),z′(t)) dtwithin the set of piecewise C1 functions (C1) that satisfy z(0)=0, z(T)=b and the constraints0⩽H(t,z(t),z′(t))⩽Pd(t) ∀t∈[0,T]In particular, we have established a necessary condition for the stationary functions of the functional. This theorem allows us to elaborate the optimization algorithm that leads to determination of the optimal functioning of the hydroplant and of the whole hydrothermal system. Finally, we present a example employing the algorithm realized to this end with the “Mathematica” package. The program developed is very simple and easy to use. [Copyright &y& Elsevier]

Consider a system comprising sensors that communicate with a remote estimator by way of a so-called collision channel. Each sensor observes a discrete random variable and must decide whether to transmit it to the remote estimator or to remain silent. The variables are independent across sensors. There is no communication among the sensors, which precludes the use of coordinated transmission policies. The collision channel functions as an ideal link when a single sensor transmits. If there are two or more simultaneous transmissions, then a collision occurs and is detected at the remote estimator. The role of the remote estimator is to form estimates of all the observations at the sensors. Our goal is to design transmission policies that are globally optimal with respect to two criteria: the aggregate probability of error, which is a convex combination of the probabilities of error in estimating the individual observations; and the total probability of error. We show that, for the aggregate probability of error criterion, it suffices to sift through a structured finite set of candidate solutions to find a globally optimal one. In general, the cardinality of this set is exponential on the number of sensors, but we discuss important cases in which it becomes quadratic or even one. For the total probability of error criterion, we prove that the solution in which each sensor transmits when it observes all but a preselected most probable value is globally optimal. So, no search is needed in this case. Our results hold irrespective of the probability mass functions of the observed random variables, regardless the size of their support. [ABSTRACT FROM AUTHOR]

We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental limitations on the performance of any distributed optimization algorithm in the presence of adversaries. We then propose a secure distributed optimization algorithm that guarantees that the nonadversarial nodes converge to the convex hull of the minimizers of their local functions under the certain conditions on the graph topology, regardless of the actions of a certain number of the adversarial nodes. In particular, we provide sufficient conditions on the graph topology to tolerate a bounded number of adversaries in the neighborhood of every nonadversarial node, and necessary and sufficient conditions to tolerate a globally bounded number of adversaries. For situations, where there are up to $F$ adversaries in the neighborhood of every node, we use the concept of maximal $F$ -local sets of graphs to provide lower bounds on the distance-to-optimality of achievable solutions under any algorithm. We show that finding the size of such sets is NP-hard. [ABSTRACT FROM AUTHOR]

A simulation model of a time-sharing system with a finite noncontiguous store and an infinite auxiliary store is used to study the variation of system parameters such as store size, number of jobs allowed to execute simultaneously, job-scheduling algorithm, etc. The effects of these variations on a measure of system performance is used to ascertain which of the parameters controllable by the job-scheduling algorithm, including the scheduling itself, require optimization, and which of the parameters not normally controllable by the scheduling algorithm have a marked effect on system performance. System performance is based upon the mean cost of delay to all jobs processed. It is shown that significant improvements in the measure of system performance can be obtained by using variable time-slice techniques and by selecting the optimum round-robin cycle time. It appears that these features would benefit from optimization whereas other parameters controllable by the scheduling algorithm affect system performance in a predictable manner and would not benefit from optimization. Features not normally under the control of the scheduling algorithm can also have a marked effect on the measure of performance; in particular, supervisor overheads, the size of the store, and the speed of the CPU. A comparison is made between the results of the simulation model and two analytical equations for quantum-oriented nonpreemptive time-sharing systems. The comparison is found to be very favorable. [ABSTRACT FROM AUTHOR]

We develop algorithms that find and track the optimal solution trajectory of time-varying convex optimization problems that consist of local and network-related objectives. The algorithms are derived from the prediction-correction methodology, which corresponds to a strategy where the time-varying problem is sampled at discrete time instances, and then, a sequence is generated via alternatively executing predictions on how the optimizers at the next time sample are changing and corrections on how they actually have changed. Prediction is based on how the optimality conditions evolve in time, while correction is based on a gradient or Newton method, leading to decentralized prediction-correction gradient and decentralized prediction-correction Newton. We extend these methods to cases where the knowledge on how the optimization programs are changing in time is only approximate and propose decentralized approximate prediction-correction gradient and decentralized approximate prediction-correction Newton. Convergence properties of all the proposed methods are studied and empirical performance is shown on an application of a resource allocation problem in a wireless network. We observe that the proposed methods outperform existing running algorithms by orders of magnitude. The numerical results showcase a tradeoff between convergence accuracy, sampling period, and network communications. [ABSTRACT FROM PUBLISHER]

We study a general class of PageRank optimization problems which involve finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are obligatory links, facultative links and forbidden links. We show that the continuous problem, as well as its discrete variant when there are no constraints coupling different pages, can both be modeled by constrained Markov decision processes with ergodic reward, in which the webmaster determines the transition probabilities of websurfers. Although the number of actions turns out to be exponential, we show that an associated polytope of transition measures has a concise representation, from which we deduce that the continuous problem is solvable in polynomial time, and that the same is true for the discrete problem when there are no coupling constraints. We also provide efficient algorithms, adapted to very large networks. Then, we investigate the qualitative features of optimal outlink strategies, and identify in particular assumptions under which there exists a “master” page to which all controlled pages should point. We report numerical results on fragments of the real web graph. [ABSTRACT FROM AUTHOR]

This work deals with trajectory optimization for a robotic sensor network sampling a spatio-temporal random field. We examine the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories. This is a high-dimensional, multi-modal, nonsmooth optimization problem, known to be NP-hard even for static fields and discrete design spaces. Under an asymptotic regime of near-independence between distinct sample locations, we show that the solutions to a novel generalized disk-covering problem are solutions to the optimal sampling problem. This result effectively transforms the search for the optimal trajectories into a geometric optimization problem. Constrained versions of the latter are also of interest as they can accommodate trajectories that satisfy a maximum velocity restriction on the robots. We characterize the solution for the unconstrained and constrained versions of the geometric optimization problem as generalized multicircumcenter trajectories, and provide algorithms which enable the network to find them in a distributed fashion. Several simulations illustrate our results. [ABSTRACT FROM AUTHOR]

We consider the problem of monitoring spatial phenomena, such as road speeds on a highway, using wireless sensors with limited battery life. A central question is to decide where to locate these sensors to best predict the phenomenon at the unsensed locations. However, given the power constraints, we also need to determine when to activate these sensors in order to maximize the performance while satisfying lifetime requirements. Traditionally, these two problems of sensor placement and scheduling have been considered separately; one first decides where to place the sensors, and then when to activate them. [ABSTRACT FROM AUTHOR]

Motivated by the need for fast computations in wireless sensor networks, the new F-Lipschitz optimization theory is introduced for a novel class of optimization problems. These problems are defined by simple qualifying properties specified in terms of increasing objective function and contractive constraints. It is shown that feasible F-Lipschitz problems have always a unique optimal solution that satisfies the constraints at equality. The solution is obtained quickly by asynchronous algorithms of certified convergence. F-Lipschitz optimization can be applied to both centralized and distributed optimization. Compared to traditional Lagrangian methods, which often converge linearly, the convergence time of centralized F-Lipschitz problems is at least superlinear. Distributed F-Lipschitz algorithms converge fast, as opposed to traditional Lagrangian decomposition and parallelization methods, which generally converge slowly and at the price of many message passings. In both cases, the computational complexity is much lower than traditional Lagrangian methods. Examples of application of the new optimization method are given for distributed estimation and radio power control in wireless sensor networks. The drawback of the F-Lipschitz optimization is that it might be difficult to check the qualifying properties. For more general optimization problems, it is suggested that it is convenient to have conditions ensuring that the solution satisfies the constraints at equality. [ABSTRACT FROM AUTHOR]

Nonlinear model predictive control (NMPC) strategies based on linearization about predicted system trajectories enable the online NMPC optimization to be performed by a sequence of convex optimization problems. The approach relies on bounds on linearization errors in order to ensure constraint satisfaction and convergence of the performance index, both during the optimization at each sampling instant and along closed loop system trajectories. This technical note proposes bounds based on robust tubes constructed around predicted trajectories. To ensure local optimality, the bounds are non-conservative for the case of zero linearization error, which requires the tube cross sections to vary along predicted trajectories. The feasibility, stability and convergence properties of the algorithm are established without the need for predictions to satisfy local optimality criteria. The strategy is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

We consider a distributed multi-agent network system where each agent has its own convex objective function, which can be evaluated with stochastic errors. The problem consists of minimizing the sum of the agent functions over a commonly known constraint set, but without a central coordinator and without agents sharing the explicit form of their objectives. We propose an asynchronous broadcast-based algorithm where the communications over the network are subject to random link failures. We investigate the convergence properties of the algorithm for a diminishing (random) stepsize and a constant stepsize, where each agent chooses its own stepsize independently of the other agents. Under some standard conditions on the gradient errors, we establish almost sure convergence of the method to an optimal point for diminishing stepsize. For constant stepsize, we establish some error bounds on the expected distance from the optimal point and the expected function value. We also provide numerical results. [ABSTRACT FROM AUTHOR]

In this technical note, the quadratic error-constrained filtering problem is formulated and investigated for discrete time-varying nonlinear systems with state delays and non-Gaussian noises. Both the Lipschitz-like and ellipsoid-bounded nonlinearities are considered. The non-Gaussian noises are assumed to be unknown, bounded, and confined to specified ellipsoidal sets. The aim of the addressed filtering problem is to develop a recursive algorithm based on the semi-definite programme method such that, for the admissible time-delays, nonlinear parameters and external bounded noise disturbances, the quadratic estimation error is not more than a certain optimized upper bound at every time step k. The filter parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures. [ABSTRACT FROM AUTHOR]