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Abstract The Expectation Maximization (EM) algorithm has been widely used for parameter estimation in data-driven process identification. EM is an algorithm for maximum likelihood estimation of parameters and ensures convergence of the likelihood function. In presence of missing variables and in ill conditioned problems, EM algorithm greatly assists the design of more robust identification algorithms. Such situations frequently occur in industrial environments. Missing observations due to sensor malfunctions, multiple process operating conditions and unknown time delay information are some of the examples that can resort to the EM algorithm. In this article, a review on applications of the EM algorithm to address such issues is provided. Future applications of EM algorithm as well as some open problems are also provided. [ABSTRACT FROM AUTHOR]

This paper proposes a new distance-based distributionally robust unit commitment (DB-DRUC) model via Kullback–Leibler (KL) divergence, considering volatile wind power generation. The objective function of the DB-DRUC model is to minimize the expected cost under the worst case wind distributions restricted in an ambiguity set. The ambiguity set is a family of distributions within a fixed distance from a nominal distribution. The distance between two distributions is measured by KL divergence. The DB-DRUC model is a “min-max-min” programming model; thus, it is intractable to solve. Applying reformulation methods and stochastic programming technologies, we reformulate this “min-max-min” DB-DRUC model into a one-level model, referred to as the reformulated DB-DRUC (RDB-DRUC) model. Using the generalized Benders decomposition, we then propose a two-level decomposition method and an iterative algorithm to address the RDB-DRUC model. The iterative algorithm for the RDB-DRUC model guarantees global convergence within finite iterations. Case studies are carried out to demonstrate the effectiveness, global optimality, and finite convergence of a proposed solution strategy. [ABSTRACT FROM AUTHOR]

In this paper, a novel multilayer backpropagation (BP) neural network model is proposed based on conjugate gradient (CG) method with generalized Armijo search. The presented algorithm requires low memory and performs fast convergent speed in practical applications. One reason is that the constructed conjugate direction guarantees the sufficient descent behavior in minimizing the given objective function. The other stems from the fact that the generalized Armijo method can automatically determine a more suitable learning rate in each training epoch. As a theoretical contribution, two deterministic convergent results, weak and strong convergence, have been detailedly proved under more relaxed assumptions. The weak convergence means that the norm of gradient of the objective function tends to zero. For the strong convergence, it represents that the sequence of weight vectors approaches a fixed point. To support the theoretical results, some illustrated simulations have been done on various benchmark datasets. [ABSTRACT FROM AUTHOR]

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies. [ABSTRACT FROM AUTHOR]

This paper presents a new sign subband adaptive filter (SSAF) algorithm with an individual-weighting-factor (IWF) for each subband, instead of a common weighting factor in the original SSAF algorithm, called the IWF-SSAF. Each individual weighting factor only depends on the corresponding subband input signal power. Compared with the SSAF algorithm, the proposed approach fully utilizes the inherent decorrelating property of subband adaptive filter for colored inputs, leading to a better convergence performance. After that, to further enhance the performance of the IWF-SSAF in a sparse system, an improved proportionate IWF-SSAF (IWF-IPSSAF) algorithm is proposed. The proposed algorithms not only inherit the good robustness of sign algorithm against impulsive interferences, but also obtain a significant improvement in the performance as compared to their counterparts (i.e., SSAF and IPSSAF), in terms of the convergence rate and tracking capability. Besides, the IWF-IPSSAF algorithm has faster convergence rate than the IWF-SSAF algorithm for sparse impulse responses. Finally, the performances of two proposed algorithms are demonstrated in the system identification and the acoustic echo cancellation with double-talk. [ABSTRACT FROM AUTHOR]

This paper develops a new framework to analyze and design iterative optimization algorithms built on the notion of integral quadratic constraints (IQCs) from robust control theory. IQCs provide sufficient conditions for the stability of complicated interconnected systems, and these conditions can be checked by semidefinite programming. We discuss how to adapt IQC theory to study optimization algorithms, proving new inequalities about convex functions and providing a version of IQC theory adapted for use by optimization researchers. Using these inequalities, we derive numerical upper bounds on convergence rates for the Gradient method, the Heavy-ball method, Nesterov's accelerated method, and related variants by solving small, simple semidefinite programming problems. We also briefly show how these techniques can be used to search for optimization algorithms with desired performance characteristics, establishing a new methodology for algorithm design. [ABSTRACT FROM AUTHOR]

Performance metrics are essential for quantifying the performance of optimization algorithms in the field of evolutionary multi-objective optimization. Such metrics allow researchers to compare different algorithms quantitatively. In the field of robust multi-objective optimization, however, there is currently no performance metric despite its significant importance. This motivates our proposal of three novel specific metrics for measuring the convergence, coverage, and success rate of robust Pareto optimal solutions obtained by robust multi-objective algorithms. The proposed metrics are employed to quantitatively evaluate and compare Robust Multi-objective Particle Swarm Optimization (RMOPSO) and Robust Non-dominated Sorting Genetic Algorithm (RNSGA-II) on seven selected benchmark problems. The results show that the proposed metrics are effective in quantifying the performance of robust multi-objective algorithms in terms of convergence, coverage, and the ratio of the robust/non-robust Pareto optimal solutions obtained. [ABSTRACT FROM AUTHOR]

Assessment of the components of a solution helps provide useful information for an optimization problem. This paper presents a new population-based problem-reduction evolutionary algorithm (PREA) based on the solution components assessment. An individual solution is regarded as being constructed by basic elements, and the concept of acceptability is introduced to evaluate them. The PREA consists of a searching phase and an evaluation phase. The acceptability of basic elements is calculated in the evaluation phase and passed to the searching phase. In the searching phase, for each individual solution, the original optimization problem is reduced to a new smaller-size problem. With the evolution of the algorithm, the number of common basic elements in the population increases until all individual solutions are exactly the same which is supposed to be the near-optimal solution of the optimization problem. The new algorithm is applied to a large variety of capacitated vehicle routing problems (CVRP) with customers up to nearly 500. Experimental results show that the proposed algorithm has the advantages of fast convergence and robustness in solution quality over the comparative algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a robust consensus algorithm is developed and sufficient conditions for convergence to consensus are proposed for a multi-agent system (MAS) with exogenous disturbances subject to partial information. By utilizingH∞robust control, differential game theory and a design-based approach, the consensus problem of the MAS with exogenous bounded interference is resolved and the disturbances are restrained, simultaneously. Attention is focused on designing anH∞robust controller (the robust consensus algorithm) based on minimisation of our proposed rational and individual cost functions according to goals of the MAS. Furthermore, sufficient conditions for convergence of the robust consensus algorithm are given. An example is employed to demonstrate that our results are effective and more capable to restrain exogenous disturbances than the existing literature. [ABSTRACT FROM PUBLISHER]

This paper presents a deterministic global optimization algorithm for solving minimax linear fractional programming (MLFP). In this algorithm, a new linearization technique is proposed, which uses more information of the objective function of the (MLFP) than other techniques. By utilizing this new linearization technique, the initial nonconvex programming problem (MLFP) is reduced to a sequence of linear relaxation programming (LRP) problems, which can provide reliable lower bound of the optimal value. The proposed algorithm is convergent to the global minimum of the (MLFP) through the successive refinement of the feasible region and solutions of a series of the (LRP). Compared with the known algorithms, numerical results show that the proposed algorithm is robust and effective. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, a new method is introduced to enhance feedback robustness against communication gain uncertainties. The method employs a fundamental property in stochastic differential equations to add a scaled stochastic dither under which tolerable gain uncertainties can be much enlarged, beyond the traditional deterministic optimal gain margin. Algorithms, stability, convergence, and robustness are presented for first-order systems. Extension to higher-dimensional systems is further discussed. Simulation results are used to illustrate the merits of this methodology. [Copyright &y& Elsevier]

A novel observer-based parameter estimation scheme with sliding mode term has been developed to estimate the road gradient and the vehicle weight using only the vehicle's velocity and the driving torque. The estimation algorithm exploits all known terms in the system dynamics and a low-pass filtered representation of the dynamics to derive an explicit expression of the parameter estimation error without measuring the acceleration. The proposed parameter estimation scheme which features a sliding-mode term to ensure the fast and robust convergence of the estimation in the presence of persistent excitation is augmented to an adaptive observer and analyzed using Lyapunov Theory. The analytical results show that the algorithm is stable and ensures finite-time error convergence to a bounded error even in the presence of disturbances. In the absence of disturbances, convergence to the true values in finite time is guaranteed. A simple practical method for validating persistent excitation is provided using the new theoretical approach to estimation. This is validated by the practical implementation of the algorithm on a small-scaled vehicle, emulating a car system. The slope gradient as well as the vehicle's mass/weight are estimated online. The algorithm shows a significant improvement over previous results. [ABSTRACT FROM AUTHOR]

Training of recurrent neural networks (RNNs) introduces considerable computational complexities due to the need for gradient evaluations. How to get fast convergence speed and low computational complexity remains a challenging and open topic. Besides, the transient response of learning process of RNNs is a critical issue, especially for online applications. Conventional RNN training algorithms such as the backpropagation through time and real-time recurrent learning have not adequately satisfied these requirements because they often suffer from slow convergence speed. If a large learning rate is chosen to improve performance, the training process may become unstable in terms of weight divergence. In this paper, a novel training algorithm of RNN, named robust recurrent simultaneous perturbation stochastic approximation (RRSPSA), is developed with a specially designed recurrent hybrid adaptive parameter and adaptive learning rates. RRSPSA is a powerful novel twin-engine simultaneous perturbation stochastic approximation (SPSA) type of RNN training algorithm. It utilizes three specially designed adaptive parameters to maximize training speed for a recurrent training signal while exhibiting certain weight convergence properties with only two objective function measurements as the original SPSA algorithm. The RRSPSA is proved with guaranteed weight convergence and system stability in the sense of Lyapunov function. Computer simulations were carried out to demonstrate applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates robust simultaneous stabilization (RSS) control method for two port-controlled Hamiltonian (PCH) systems and proposes results on the design of simultaneous stabilization controller with parameters for such systems. Firstly, two PCH systems are studied. Using the dissipative Hamiltonian structural properties, the systems are combined to generate an augmented PCH system. When there are external disturbances in the systems, a robust controller with parameters is designed for the systems. Secondly, an algorithm for solving parameters of the controller is proposed with symbolic computation. Finally, an illustrative example is presented to show that the RSS controller obtained in this paper works very well. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a distributed algorithmic solution, termed Coalition formation and deployment algorithm , to achieve network configurations where agents cluster into coincident groups that are distributed optimally over the environment. The motivation for this problem comes from spatial estimation tasks executed with unreliable sensors. We propose a probabilistic strategy that combines a repeated game governing the formation of coalitions with a spatial motion component governing their location. For a class of probabilistic coalition switching laws, we establish the convergence of the agents to coincident groups of a desired size in finite time and the asymptotic convergence of the overall network to the optimal deployment, both with probability 1. We also investigate the algorithm’s time and communication complexity. Specifically, we upper bound the expected completion time of executions that use the proportional-to-number-of-unmatched-agents coalition switching law under arbitrary and complete communication topologies. We also upper bound the number of messages required per timestep to execute our strategy. The proposed algorithm is robust to agent addition and subtraction. From a coalitional game perspective, the algorithm is novel in that the players’ information is limited to the neighboring clusters. From a motion coordination perspective, the algorithm is novel because it brings together the basic tasks of rendezvous (individual agents into clusters) and deployment (clusters in the environment). Simulations illustrate the correctness, robustness, and complexity results. [Copyright &y& Elsevier]

Abstract: The competitiveness of a container terminal is highly conditioned by the time that container vessels spend on it. The proper scheduling of the quay cranes can reduce this time and allows a container terminal to be more attractive to shipping companies. The goal of the Quay Crane Scheduling Problem (QCSP) is to minimize the handling time of the available quay cranes when performing the tasks of loading and unloading containers onto/from a container vessel. This paper proposes a hybrid Estimation of Distribution Algorithm with local search to solve the QCSP. This approach includes a priori knowledge about the problem in the initialization step to reach promising regions of the search space as well as a novel restarting strategy with the aim of avoiding the premature convergence of the search. Furthermore, an approximate evaluation scheme is applied in order to reduce the computational burden. Moreover, its performance is statistically compared with the best optimization method from the literature. Numerical testing results demonstrate the high robustness and efficiency of the developed technique. Additionally, some relevant components of the scheme are individually analyzed to check their effectiveness. [Copyright &y& Elsevier]

Abstract: Multi-frame blind restoration algorithms often have disadvantages of slow convergence and sensitiveness to complex noises. In this paper, we proposed a new multi-frame method based on PSF estimate and TV regularization. Our algorithm consists of first simplifying the multi-frame MAP model through the identification of blur parameters for each frame image and then adding various penalty terms to speed up the convergence in deconvolution process obviously. Finally, an adaptive L2/L1 norm selection scheme is built to deal with various noise distributions. A series of experiment results show that the proposed method can outperform other previous work robustly and efficiently even under large noise and image blurring. [Copyright &y& Elsevier]

The paper proposes application of Bat algorithm for solving economic load dispatch problem. Bat algorithm is based on the echolocation characteristics of micro bats. The proposed approach was examined and tested with the numerical results of Economic load Dispatch (ED) problems with three and five generating units with valve-point loading without considering prohibited operating zones and ramp rate limits. The results of the proposed Bat algorithm are compared with that of the other techniques such as lambda iteration, GA, PSO, APSO and ABC. For both the cases, the proposed algorithm outperforms the solution reported for the existing algorithms. In addition, the promising results show the robustness, fast convergence and efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the consistency and consensus of reciprocal [0,1]-valued preference relations (also called fuzzy preference relations by many authors) based on the multiplicative consistency property, which is an important issue in fuzzy set theory. An algorithm is first developed to improve the consistency level of a reciprocal [0,1]-valued preference relation, and the corresponding algorithm for the incomplete reciprocal [0,1]-valued preference relation is also developed. We further propose the consensus improving algorithms for individual reciprocal [0,1]-valued preference relations or incomplete ones. The convergence and robustness of the algorithms are proven and some important conclusions are obtained. In addition, the proposed algorithms can improve the consistency or consensus of reciprocal [0,1]-valued preference relations with less interactions with the decision makers, which can save a lot of time and obtain the results quickly. [Copyright &y& Elsevier]

SUMMARY Machine learning over fully distributed data poses an important problem in peer-to-peer applications. In this model, we have one data record at each network node but without the possibility to move raw data because of privacy considerations. For example, user profiles, ratings, history, or sensor readings can represent this case. This problem is difficult because there is no possibility to learn local models; the system model offers almost no guarantee for reliability, yet the communication cost needs to be kept low. Here, we propose gossip learning, a generic approach that is based on multiple models taking random walks over the network in parallel, while applying an online learning algorithm to improve themselves, and getting combined via ensemble learning methods. We present an instantiation of this approach for the case of classification with linear models. Our main contribution is an ensemble learning method, which-through the continuous combination of the models in the network-implements a virtual weighted voting mechanism over an exponential number of models at practically no extra cost as compared with independent random walks. We prove the convergence of the method theoretically, and perform extensive experiments on benchmark data sets. Our experimental analysis demonstrates the performance and robustness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of row straightening of agents via local interactions. A nonlinear control protocol that ensures finite-time equidistant allocation on a segment is proposed. With the designed protocol, any settling time can be guaranteed regardless of the initial conditions. A robust modification of the control algorithm based on sliding mode control technique is presented. The case of multidimensional agents is also considered. The theoretical results are illustrated via numerical simulations. [ABSTRACT FROM AUTHOR]

This paper provides a mathematical framework for modelling collaborative reputation systems (CRSs), which are useful in many fields of electronic commerce. A CRS is an algorithm that, at discrete points in time, receives in input from a set of users some ratings of a set of objects and generates a reputation for both the raters and the evaluated objects. Sufficient conditions for the convergence of a CRS are given, using basic results of the fixed point theory, and in particular for a broad class of iterative filtering methods and their related CRSs, generalizing some previous results. Finally, we analyse a simple kind of CRS which allows to use a priori information on the reliability of a subset of raters. Experimental results provide evidence that such CRSs exhibit high level of robustness against unfair raters. [ABSTRACT FROM AUTHOR]

Iterative data-based controller tuning consists of iterative adjustment of the controller parameters towards the parameter values which minimise an H 2 performance criterion. The convergence to the global minimum of the performance criterion depends on the initial controller parameters and on the step size of each iteration. This article presents convergence properties of iterative algorithms when they are affected by disturbances. [ABSTRACT FROM PUBLISHER]

Abstract: The Thick Level Set (TLS) model is a damage model containing a non-local treatment that prevents from spurious localization issues. It also offers an automatic transition from damage to fracture. The TLS approach to model damage growth was first presented in Möes et al. with a first numerical implementation for a time-dependent damage evolution law. In this paper, we propose some improvements in terms of discretization and explicit damage growth algorithms to obtain a robust, efficient and easy-to-implement model. These improvements include a simple and efficient variational formulation for computing the non-local quantities as well as the introduction of a so-called ramped Heaviside enrichment function to properly take into account the transition to cracks in fully damaged zones. We consider here a simple explicit formulation for quasi-static loadings, decoupling the elastic computation and the damage growth. The method is validated through standard benchmarks and compared to the Griffith’s fracture theory. The convergence of energy and displacement errors is observed. More complex computations including damage initiations are eventually performed. [Copyright &y& Elsevier]

The state-of-the-art interactive image segmentation algorithms are sensitive to the user inputs and often unable to produce an accurate boundary with a small amount of user interaction. They frequently rely on laborious user editing to refine the segmentation boundary. In this paper, we propose a robust and accurate interactive method based on the recently developed continuous-domain convex active contour model. The proposed method exhibits many desirable properties of an effective interactive image segmentation algorithm, including robustness to user inputs and different initializations, the ability to produce a smooth and accurate boundary contour, and the ability to handle topology changes. Experimental results on a benchmark data set show that the proposed tool is highly effective and outperforms the state-of-the-art interactive image segmentation algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Feedforward neural networks (FNNs) have been extensively applied to various areas such as control, system identification, function approximation, pattern recognition etc. A novel robust control approach to the learning problems of FNNs is further investigated in this study in order to develop efficient learning algorithms which can be implemented with optimal parameter settings and considering noise effect in the data. To this aim, the learning problem of a FNN is cast into a robust output feedback control problem of a discrete time-varying linear dynamic system. New robust learning algorithms with adaptive learning rate are therefore developed, using linear matrix inequality (LMI) techniques to find the appropriate learning rates and to guarantee the fast and robust convergence. Theoretical analysis and examples are given to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper we propose a new methodology to synthesize and implement robust monotonically convergent ILC for lifted systems, with the computational complexity that is linear in the trial length. Starting from the model uncertainty of the local sample to sample LTI or LTV models, and using the randomized algorithm, we compute the bound on the model uncertainty of the ILC system representation in the trial domain (lifted ILC). Based on this computed uncertainty bound, we design weighting matrices of the Norm Optimal ILC, such that the robust monotonic convergence condition is satisfied. Since we compute the uncertainty bound, rather than assuming its value in the trial domain, we reduce the conservatism of the robust design. The linear computational complexity of the algorithms for computation of the uncertainty bound and implementation of the Norm Optimal ILC law, is achieved through exploiting the sequentially semi-separable structure of the lifted system matrices. Therefore the framework proposed in this paper is especially suitable for the LTI and LTV uncertain systems with a large number of samples in the trial. We have performed numerical experiments to demonstrate the robustness and linear computational complexity of the proposed method. [Copyright &y& Elsevier]

Abstract: A simple but effective on-line method to estimate the delay from step response, which can be used for stable, unstable and integrating systems, is proposed in this paper. The estimation and control are made simultaneously since the nominal delay is updated in closed-loop based on certain calculus on the output signal. Moreover, the approach is based on a Modified Smith Predictor and the delay estimation is implemented using a multi-model scheme with fixed models. Additionally, the convergence properties of the estimation algorithm and the stability analysis of the closed-loop are well-defined. Simulation examples show the effectiveness of the proposed method, where the delay estimation leads to an optimal and robust controller, tackling the uncertainty in the delay. [Copyright &y& Elsevier]

Abstract: Mitigation of the effects of tonal noise and vibration has importance across a wide range of application domains. For low frequency disturbances, active control methodologies have proven to be highly effective when coupled with harmonic algorithms that target specific problematic frequencies. In this paper a novel harmonic control approach is presented that combines a classical exponential forgetting recursive least squares (ExF-RLS) estimator with an optimal gradient descent update law. The paper provides a rigorous proof that with a sinusoidal reference, the ExF-RLS estimator can be approximated by a fixed parameter filter and that the accuracy of the approximation is dependent upon the values of both the forgetting factor and the sampling frequency. With this approximation it is also proven that the complete iterative frequency domain harmonic control algorithm, when used with an instantaneous update, can be accurately represented by a linear time-invariant (LTI) feedback compensator. Such representations have clear importance since the stability, performance, convergence and robustness properties of the adaptive system can thereby be examined using well-established LTI analysis tools. The algorithm and the analytical results described above are illustrated in the paper using an experimental active vibration isolation mount that has been developed for marine systems application. [Copyright &y& Elsevier]

Beamforming with sparse constraint has shown important performance improvement. In this paper, a robust least squares constant modulus beamforming with sparse constraint is proposed. The proposed approach shows a faster convergence performance, lower sidelobe level, and better steady-state output signal-to-interference-plus-noise ratio (SINR) than that of the conventional linearly constrained least squares constant modulus algorithm, especially in the presence of mismatches between the actual and presumed steering vectors. Simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods constitute excellent neural network training methods which are characterized by their simplicity and their very low memory requirements. In this paper, we propose a new spectral conjugate gradient method which guarantees sufficient descent using any line search, avoiding thereby the usually inefficient restarts. Moreover, we establish the global convergence of our proposed method under some assumptions. Experimental results provide evidence that our proposed method is preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness. [ABSTRACT FROM AUTHOR]

Abstract: Various sparse principal component analysis (PCA) methods have recently been proposed to enhance the interpretability of the classical PCA technique by extracting principal components (PCs) of the given data with sparse non-zero loadings. However, the performance of these methods is prone to be adversely affected by the presence of outliers and noises. To alleviate this problem, a new sparse PCA method is proposed in this paper. Instead of maximizing the L 2-norm variance of the input data as the conventional sparse PCA methods, the new method attempts to capture the maximal L 1-norm variance of the data, which is intrinsically less sensitive to noises and outliers. A simple algorithm for the method is specifically designed, which is easy to be implemented and converges to a local optimum of the problem. The efficiency and the robustness of the proposed method are theoretically analyzed and empirically verified by a series of experiments implemented on multiple synthetic and face reconstruction problems, as compared with the classical PCA method and other typical sparse PCA methods. [Copyright &y& Elsevier]

The special importance of Difference of Convex (DC) functions programming has been recognized in recent studies on nonconvex optimization problems. In this work, a class of DC programming derived from the portfolio selection problems is studied. The most popular method applied to solve the problem is the Branch-and-Bound (B&B) algorithm. However, "the curse of dimensionality" will affect the performance of the B&B algorithm. DC Algorithm (DCA) is an efficient method to get a local optimal solution. It has been applied to many practical problems, especially for large-scale problems. A B&B-DCA algorithm is proposed by embedding DCA into the B&B algorithms, the new algorithm improves the computational performance and obtains a global optimal solution. Computational results show that the proposed B&B-DCA algorithm has the superiority of the branch number and computational time than general B&B. The nice features of DCA (inexpensiveness, reliability, robustness, globality of computed solutions, etc.) provide crucial support to the combined B&B-DCA for accelerating the convergence of B&B. [ABSTRACT FROM AUTHOR]

Abstract: The Fuzzy c-means clustering (FCM) algorithm is sensitive to noises and outliers and tends to get local optimal solutions. The Possibilistic Fuzzy C-Means (PFCM) clustering algorithm and the Improved Possibilistic C-Means (IPCM) clustering algorithm are resistant to noises but consume too much time because of the slow convergence and what is more, they are not robust enough to noises. To overcome these defects, this paper proposes a sampleweighted robust fuzzy c-means clustering algorithm which calculates the weight for each sample. The outliers will receive much lower weights and their effect on cluster centers is restrained and thus robustness is achieved. The experimental results show the effectiveness of the algorithm. In addition, the idea of calculating weights for samples can be applied to other fuzzy clustering algorithms to form new robust algorithms. [Copyright &y& Elsevier]

The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross nonlinearities applied to the measurements. In this paper we introduce a new algorithm—restricted-step shrinkage (RSS)—to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for nonconvex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest. [ABSTRACT FROM AUTHOR]

Abstract: Reduced-space barrier NLP algorithms are particularly useful for optimization of large structured systems with few degrees of freedom. Such optimization algorithms are often applied on process models developed within equation oriented process simulators. By partitioning the search direction into tangential and normal steps, these methods can exploit the structure of the equality constraints and adjust the remaining degrees of freedom in a lower dimensional space. Moreover, as shown in previous work, the barrier approach extended with a novel filter linear search algorithm has global and fast local convergence properties. However, convergence properties of the reduced-space barrier algorithm require regularity assumptions. In particular, the method may fail in the presence of linearly dependent active constraints. To deal with these questions, we modify the reduced-space barrier method in two ways. First, as the filter line search requires a feasibility restoration step, we develop and analyze an improved algorithm for this step, which is tailored to the reduced-space method. In addition, a dimension change procedure is proposed to address decomposition of problems with linearly dependent constraints. Finally, both approaches are implemented within a reduced-space version of IPOPT and numerical tests demonstrate the performance of the proposed modifications. [Copyright &y& Elsevier]

Abstract: We investigate the benefits of estimating the group delay spectrum (as opposed to the phase spectrum) on the performance of an adaptive laser pulse shaping experiment. We use both numerical and experimental approaches, and consider different figures of merit such as efficiency, noise robustness, convergence speed, repeatability, fitness sensitivity, and parameter insensitivity. While primarily focused on the process of broadband second harmonic generation, we also study a resonant third order nonlinear process. Our results show an overall superiority of delay-based formulation in the cases under study (compared to a conventional phase-based formulation) for adaptive laser pulse shaping. [Copyright &y& Elsevier]

A constrained moving horizon observer is developed for nonlinear discrete-time systems. The algorithm is proved to converge exponentially under a detectability assumption with the data being exciting at all times. However, in many practical estimation problems, such as combined state and parameter estimation, the data may not be exciting for every period of time. The algorithm therefore has regularisation mechanisms to ensure robustness and graceful degradation of performance in cases when the data are not exciting. This includes the use of a priori estimates in the moving horizon cost function, and the use of thresholded singular value decomposition to avoid ill-conditioned or ill-posed inversion of the associated nonlinear algebraic equations that define the moving horizon cost function. The latter regularisation relies on monitoring of the rank of an estimate of a Hessian-like matrix and conditions for uniform exponential convergence are given. The method is in particular useful with augmented state space models corresponding to mixed state and parameter estimation problems, or dynamics that are not asymptotically stable, as illustrated with two simulation examples. [ABSTRACT FROM AUTHOR]

Abstract: We present an improved iteration regularization method for solving linear inverse problems. The algorithm considered here is detailedly given and proved that the computational costs for the proposed method are nearly the same as the Landweber iteration method, yet the number of iteration steps by the present method is even less. Meanwhile, we obtain the optimum asymptotic convergence order of the regularized solution by choosing a posterior regularization parameter based on Morozov’s discrepancy principle, and the present method is applied to the identification of the multi-source dynamic loads on a surface of the plate. Numerical simulations of two examples demonstrate the effectiveness and robustness of the present method. [Copyright &y& Elsevier]

A globally convergent optimization algorithm for solving large nonlinear optimal power flow (OPF) problems is presented. As power systems become heavily loaded, there is an increasing need for globally convergent OPF algorithms. By global convergence, one means the optimization algorithm being able to converge to an OPF solution, if at least one exists, for any choice of initial point. The globally convergent OPF presented is based on an infinity-norm trust region approach, using interior-point methods to solve the trust region subproblems. The performance of the proposed trust region interior-point OPF algorithm, when applied to the IEEE 30-, 57-, 118-, and 300-bus systems, and to an actual 1211-bus system, is compared with that of two widely used nonlinear interior-point methods, namely, a pure primal-dual and its predictor-corrector variant. [ABSTRACT FROM PUBLISHER]

The convergence properties of the iterative water-filling (IWF) based algorithms have been derived in the ideal situation where the transmitters in the network are able to obtain the exact value of the interference plus noise (IPN) experienced at the corresponding receivers in each iteration of the algorithm. However, these algorithms are not robust because they diverge when there is time-varying estimation error of the IPN, a situation that arises in real communication system. In this correspondence, we propose an algorithm that possesses convergence guarantees in the presence of various forms of such time-varying error. Moreover, we also show by simulation that in scenarios where the interference is strong, the conventional IWF diverges while our proposed algorithm still converges. [ABSTRACT FROM AUTHOR]

Channel order estimation is a critical task for blind system identification. The performance of the blind system identification algorithms depends on the accuracy and robustness of the channel order estimation. In this paper, a new effective channel order estimation algorithm with high accuracy and robustness is proposed for single-input multi-output (SIMO) systems. The proposed algorithm is guaranteed to find the true channel order for the noise-free case and it performs significantly better than the alternative algorithms for noisy observations. This algorithm shows a consistent performance when the number of observations, channels and channel order are changed. The proposed algorithm is integrated with the least squares smoothing (LSS) algorithm for blind identification of the channel coefficients. Comparisons are done with a variety of different algorithms including linear prediction (LP) based methods. It is shown that significant gain can be obtained compared to the alternative approaches in effective channel order estimation. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new support vector machine (SVM) called dual margin Lagrangian support vectors machine (DMLSVM). Unlike other SVMs which use only support vectors to determine the separating hyperplanes, DMLSVM utilizes all the available training data for training the classifier, thus producing robust performance. The training data are weighted differently depending on whether they are in a marginal region or surplus region. For fast training, DMLSVM borrows its training algorithm from Lagrangian SVM (LSVM) and tailors the algorithm to its formulation. The convergence of our training method is rigorously proven and its validity is tested on a synthetic test set and UCI dataset. The proposed method can be used in a variety of applications such as a recommender systems for web contents of IPTV services. [ABSTRACT FROM AUTHOR]

Affine projection (AP) algorithms have been proposed in recent years for use in active noise control systems. This is due to their potential high convergence speed along with their robustness and moderate computational cost. However, these algorithms can exhibit an excessive computational cost for high projection orders (just when higher convergence speed is achieved). Thus, computationally efficient versions of these algorithms have been proposed. For the particular case of the AP algorithms applied to active noise control, the use of the conventional filtered-x structure instead of the commonly used modified filtered-x method can be understood as an efficient strategy, since it needs fewer operations to update the adaptive filter coefficients. However, the use of this structure implies different algorithm behavior for the following two reasons: the signals needed in the coefficient updates do not correspond exactly to the AP algorithm and this structure introduces a delay between the update of the adaptive filter coefficients and its effect on the noise signal. In practice, this dual effect mainly affects convergence of the algorithms in the transient regime. This correspondence presents a mathematical model so that the transient behavior of the conventional filtered-x AP algorithm can be predicted from the reference signal statistics and algorithm parameters. [ABSTRACT FROM PUBLISHER]

Abstract: The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. This paper presents a variation on the standard PSO algorithm called the rank based particle swarm optimizer, or PSOrank, employing cooperative behavior of the particles to significantly improve the performance of the original algorithm. In this method, in order to efficiently control the local search and convergence to global optimum solution, the best particles are taken to contribute to the updating of the position of a candidate particle. The contribution of each particle is proportional to its strength. The strength is a function of three parameters: strivness, immediacy and number of contributed particles. All particles are sorted according to their fitness values, and only the best particles will be selected. The value of decreases linearly as the iteration increases. A time-varying inertia weight decreasing non-linearly is introduced to improve the performance. PSOrank is tested on a commonly used set of optimization problems and is compared to other variants of the PSO algorithm presented in the literature. As a real application, PSOrank is used for neural network training. The PSOrank strategy outperformed all the methods considered in this investigation for most of the functions. Experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness. [ABSTRACT FROM AUTHOR]