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Formulating a control design for integer-valued inputs might be advantageous over, for example, rounding strategies based on a real-valued solution. However, the speed of convergence, computational...

In general, infill sampling is the core process of efficient global optimization (EGO). Research on infill sampling with few points, high convergence speed and simplicity has received increasing at...

We propose an inexact nonmonotone successive quadratic programming (SQP) algorithm for solving nonlinear programming problems with equality constraints and bounded variables. Regarding the value of...

Obtaining a specific region from the efficient front for multi-objective and practical optimization problems helps decision-makers. Reference point approaches are suggested to reach the region of i...

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is used in the form of a piece-wise linear model of the objective function, which provides us with much better prediction abilities as compared with the standard linear model. To the best of our knowledge, this approach was never really applied in Convex Minimization to differentiable functions in view of the high complexity of the corresponding auxiliary problems. However, we show that all necessary computations can be done very efficiently. Consequently, we get new optimization methods, which are better than the usual Gradient Methods both in the number of oracle calls and in the computational time. Our theoretical conclusions are confirmed by preliminary computational experiments., Comment: This is an Accepted Manuscript of an article published by Taylor \& Francis in Optimization Methods and Software on 13 Jan 2021, available at https://www.tandfonline.com/doi/10.1080/10556788.2020.1858831

Traffic assignment is used for infrastructure planning, based on metrics like total system travel time (TSTT), vehicle-miles traveled (VMT) and link or path flows. Algorithms for traffic assignment...

Travel time and monetary cost are the two important factors influencing travelers’ route choice behavior. Rather than combining them together as a single objective, a bi-objective user equilibrium ...

This paper investigates the convergence characteristics of the conventional P-type iterative learning control (ILC) scheme and exploits a gain-adaptive iterative learning control mechanism for a cl...

This paper concentrates on the suboptimal state estimation problem for systems without acknowledgement (ACK). The ACK signal is used for informing the estimator of whether control-input packets hav...

Butterfly Optimisation Algorithm (BOA) is a kind of meta-heuristic swarm intelligence algorithm based on butterfly foraging strategy, but it still needs to be improved in the aspects of convergence...

The alternating direction method of multipliers (ADMM) is a classical effective method for solving two-block convex optimization subject to linear constraints. However, its convergence may not be g...

In spite of being one of the most popular optimization methods, Nelder–Mead's simplex search algorithm with the default choice of parameters performs poorly on high-dimensional problems. The work p...

To improve the convergence of multiple-site weather generators (SWGs) based on the brute force algorithm (MBFA), a genetic algorithm (GA) is proposed to search the overall optimal correlati...

Two transformations of gradient-descent iterative methods for solving unconstrained optimization are proposed. The first transformation is called modification and it is defined using a small enlargement of the step size in various gradient-descent methods. The second transformation is termed as hybridization and it is defined as a composition of gradient-descent methods with the Picard–Mann hybrid iterative process. As a result, several accelerated gradient-descent methods for solving unconstrained optimization problems are presented, investigated theoretically and numerically compared. The proposed methods are globally convergent for uniformly convex functions satisfying certain condition under the assumption that the step size is determined by the backtracking line search. In addition, the convergence on strictly convex quadratic functions is discussed. Numerical comparisons show better behaviour of the proposed methods with respect to some existing methods in view of the Dolan and Moré's performance profile with respect to all analysed characteristics: number of iterations, the CPU time, and the number of function evaluations.

This paper studies the no-arbitrage pricing of the "Polaris Income Plus Daily" structured in the "Polaris Choice IV" variable annuities recently issued by the American International Group. Distinct from the withdrawal benefits studied in the literature, Polaris allows the income base to "lock in" the high water mark of the investment account over a certain monitoring period which is related to the timing of policyholder's first withdrawal. By prudently introducing certain auxiliary state and decision variables, we manage to formulate the pricing model under a Markovian stochastic optimal control framework. By a slight modification of the fee structure, we show the existence of a bang-bang solution to the stochastic control problem: the optimal withdrawal strategy is among a few explicit choices. We consequently design a novel Least Squares Monte Carlo (LSMC) algorithm to approach the optimal solution. Convergence results are established for the algorithm by applying the theory of nonparametric sieve estimation. Compared with existing LSMCs, our algorithm possesses a number of advantages such as memory reduction, preserving convexity and monotonicity of the continuation value, reducing the computational cost of the tuning parameter selection, and evading extrapolating value function estimate. Finally, we prove that the obtained pricing result works as an upper bound of the no-arbitrage price of Polaris with the real fee structure. Numerical experiments show that this upper bound is fairly tight.

Both stochastic and deterministic models can be used to describe the day-to-day evolution of traffic flow across a network, and applied for a raft of transport planning and control purposes. We mig...

In this paper, we consider consensus control of high-order multi-agent systems with antagonistic interactions and unknown disturbances. The interaction topology associated with the multi-agent system is described by a coopetition network. Linearly parameterized approaches are used to model the unknown disturbances. Some novel transformations are presented to design the distributed adaptive controllers, which guarantees that a bipartite consensus can be achieved for all the agents. At the same time, convergence of the bipartite consensus error is analyzed with the help of signed graph theory and the Barbalat's Lemma. Some simulation results are also provided to demonstrate the effectiveness of the proposed adaptive control strategy.

Most of the software that is available to implement Bayesian approaches uses Markov chain Monte Carlo (MCMC) methods. It is our impression that many researchers are primarily concerned with converg...

Water cycle algorithm (WCA) is a population-based metaheuristic algorithm, inspired by the water cycle process and movement of rivers and streams towards sea. The WCA shows good performance in both...

Considering that a supply chain comprises several independent decision makers, a supply chain network equilibrium model that consists of manufacturers, retailers and consumers is developed. After a...

Published online: 29 Aug 2018, A number of first-order methods have been proposed for smooth multiobjective optimization for which some form of convergence to first-order criticality has been proved. Such convergence is global in the sense of being independent of the starting point. In this paper, we analyse the rate of convergence of gradient descent for smooth unconstrained multiobjective optimization, and we do it for non-convex, convex, and strongly convex vector functions. These global rates are shown to be the same as for gradient descent in single-objective optimization and correspond to appropriate worstcase complexity bounds. In the convex cases, the rates are given for implicit scalarizations of the problem vector function., Support for A.I.F. Vaz was partially provided by FCT [grant number COMPETE:POCI-01- 0145-FEDER-007043], [grant number UID/CEC/00319/2013], and support for L.N. Vicente was partially provided by FCT [grant number UID/MAT/00324/2013], [grant number P2020 SAICTPAC/0011/2015.]

This paper addresses convergence issue of two networked iterative learning control (NILC) schemes for a class of discrete-time nonlinear systems with random packet dropout occurred in input and out...

Quasi-convex optimization is fundamental to the modelling of many practical problems in various fields such as economics, finance and industrial organization. Subgradient methods are practical iter...

Real world problems are embedded with uncertainties. Therefore, to tackle these problems, one must consider probabilistic nature of the problems both in modeling and solution. In this work, concept...

Appropriate delineation of rain gauge stations is a classic problem in operational hydrology. The current literature on rain gauge network design considers various simplifications to bypass the curse of dimensionality. This paper presents a new methodology for optimum rain gauge network design with no simplification involved. To the best of the authors’ knowledge, this is the first time whereby geostatistical tools are coupled with artificial bee colony (ABC) to prioritize rain gauge stations. To evaluate the effectiveness of the proposed methodology, the coupled algorithm is applied to a case study with 34 existing rain gauge stations in the south-western part of Iran. The developed methodology is quite robust, efficient and fills a gap in existing methodologies. It has few control parameters, therefore accelerating the convergence speed remarkably. The results show that the proposed approach compares well with existing paradigms in rain gauge network design. In particular, the measure of network...

An efficient trajectory optimisation approach combining the classical control variable parameterisation (CVP) with a novel smooth technology and two penalty strategies is developed to solve the trajectory optimal control problems. Since it is difficult to deal with path constraints in CVP method, the novel smooth technology is firstly employed to transform the complex constraints into one smooth constraint. Then, two penalty strategies are proposed to tackle the converted path and terminal constraints to decrease the computational complexity and improve the constraints satisfaction. Finally, a nonlinear programming problem, which approximates the original trajectory optimisation problem, is obtained. Error analysis shows that the proposed method has good convergence property. A general hypersonic cruise vehicle trajectory optimisation example is employed to test the performance of the proposed method. Numerical results show that the path and terminal conditions are well satisfied and better trajec...

Transient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many design variables are involved and hundreds of iterations are usually required for convergence. This article aims to provide an efficient quadratic approximation for multi-material topology optimization of transient heat conduction problems. Reciprocal-type variables, instead of relative densities, are introduced as design variables. The sequential quadratic programming approach with explicit Hessians can be utilized as the optimizer for the computationally demanding optimization problem, by setting up a sequence of quadratic programs, in which the thermal compliance and weight can be explicitly approximated by the first and second order Taylor series expansion in terms of design variables. Numerical examples show clearly that the present approach can achieve better performance in terms of computational efficiency and iteration number than the sol...

Recent studies have confirmed that travelers consider travel time reliability in addition to average travel time when making route choice decisions. In this study, we develop a bi-objective routing model that seeks to simultaneously optimize the average travel time and travel time reliability. The semi-standard deviation (SSD) is chosen as the reliability measure because it reflects travelers' concerns over longer travel time better than the commonly used standard deviation. The Pareto-optimal solutions to the bi-objective model are found by using an improved strength Pareto evolutionary algorithm. Tests on a real-world urban network with field measured travel time data have demonstrated good performance of the algorithm in the aspects, such as computational efficiency, quick convergence, and closeness to the global Pareto-optimal. Overall, the bi-objective routing model generates reasonable path recommendations. The SSD-based model is sensitive to the asymmetry of travel time distribution and ten...

The influence of various heterogeneous parameters, stochastic uncertain factors, and pollutant particles from the industrial effluents in the water system is investigated using advection dispersion equation (ADE) and the Bayesian approximation. Here, the decay coefficient is decomposed into the exact part and the deviation part. The coefficient is used to find out the errors and deviation in decay during the flow of pollutants. Two Bayesian models are developed to analyze the posterior distributions and to find out the Bayes factor for the stochastic covariance estimation. The Bayesian calibration focused the characteristics of both on mechanistic and statistical approximation. The efficiency and accuracy of the developed models are checked from the results obtained on the basis of the confidence interval. Markov chain Monte Carlo simulation is used to acquire the convergence point of parameters for the posterior estimation. The stochastic covariance or white noise represents the effect of random ...

In order to cope with system disturbances in multi-phase batch processes with different dimensions, a hybrid robust control scheme of iterative learning control combined with feedback control is proposed in this paper. First, with a hybrid iterative learning control law designed by introducing the state error, the tracking error and the extended information, the multi-phase batch process is converted into a two-dimensional Fornasini–Marchesini (2D-FM) switched system with different dimensions. Second, a switching signal is designed using the average dwell-time method integrated with the related switching conditions to give sufficient conditions ensuring stable running for the system. Finally, the minimum running time of the subsystems and the control law gains are calculated by solving the linear matrix inequalities. Meanwhile, a compound 2D controller with robust performance is obtained, which includes a robust extended feedback control for ensuring the steady-state tracking error to converge rap...

We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a sequence of representative models of the objective function. Using the new information gathered from those multiple points, a local step is gradually improved by updating its direction as well as its length. We give a global convergence result and also provide the parallel implementation details accompanied with a numerical study. Our numerical study shows that the proposed algorithm is a promising alternative as a globalization strategy.

This paper presents a generalised time-synchronous gossip-based algorithm for solving distributed optimisation problems associated with multi-agent networked systems. The proposed algorithm presents a generalisation such that the optimisation process can operate in the entire spectrum from ‘complete consensus’ to ‘complete disagreement’. A user-defined control parameter θ is identified for controlling such tradeoff as well as the temporal convergence properties. We formulate the algorithm based upon generalised time-synchronous gossip algorithm and subgradient method and provide analytical results for first and second moment convergence analysis. The proposed algorithm also provides a convergence rate estimate of O(1/m) in the number of iterations m when the step size is constant. We consider the effect of noise in networked systems from the perspectives of modelling uncertainty and measurement noise in subgradient estimation process and communication among agents, respectively. A numerical case s...

The numerical solution of MHD flow of fractional viscoelastic fluid is considered in this article. The main purpose of this work is to construct and analyze stable and high order scheme to efficien...

Differential evolution (DE) is one of the popular techniques in large-scale portfolio optimization, which is noticed for its applications in the problems that are non-convex, non-continuous, non-differentiable, and so on. This technique suffers specific short-comings, for example, unstable convergence in the final solution, trapped in local optimum, and demand for high number of replications. Optimal Computing Budget Allocation (OCBA) technique gives an efficient way to reach the global optimum by optimally assigning computing resource among designs. The integration of DE and OCBA gives better performance than DE alone in terms of convergence rate and the attained global optimum. The ordering of the integration also plays a vital role, that is, the strategy of first applying DE before OCBA outperforms the reversely ordered one. Both integration strategies are essentially the improved DE algorithms for large-scale portfolio optimization. In addition to numerical tests, empirical analysis of 100 stocks in S&P500 over a 10-year period confirms the conclusions.

To minimize makespan in the permutation flow shop scheduling problem, a modified immunoglobulin-based artificial immune system algorithm (M-IAIS) is developed to search for a job sequence. The basic structure of immunoglobulin-based artificial immune system algorithm consists of three parts, somatic recombination, hypermutation, and isotype switching. A special process, named B cell repertoire updating, is considered in M-IAIS algorithm to accelerate the convergence speed. Taillard’s benchmark problems are chosen as test instances. Percentage deviation, hypothesis test, convergence performance, and robust analysis are considered in the paper to evaluate the performance of M-IAIS algorithm. Computational results show that M-IAIS algorithm is competitive for the permutation flow shop scheduling problem.

This paper develops and suggests fast convergence evolutionary programming (FCEP) for solving multi-area economic dispatch problem with tie-line constraints, transmission losses, multiple f...

In this paper we describe and analyse new computational technique for solving proximal split feasibility problem (SFP) using a modified proximal split feasibility algorithm. The two convex and lower semi-continuous objective functions are assumed to be non-smooth. Some application to SFP are given. We demonstrate the computational efficiency of the proposed algorithm with nontrivial numerical experiments. We also compare our method with other relevant methods in the literature in terms of convergence, stability, efficiency and implementation with our illustrative numerical examples.

The paper proposes a new shrinking gradient-like projection method for solving equilibrium problems. The algorithm combines the generalized gradient-like projection method with the monotone hybrid method. Only one optimization program is solved onto the feasible set at each iteration in our algorithm without any extra-step dealing with the feasible set. The absence of an optimization problem in the algorithm is explained by constructing slightly different cutting-halfspace in the monotone hybrid method. Theorem of strong convergence is established under standard assumptions imposed on equilibrium bifunctions. An application of the proposed algorithm to multivalued variational inequality problems (MVIP) is presented. Finally, another algorithm is introduced for MVIPs in which we only use a value of main operator at the current approximation to construct the next approximation. Some preliminary numerical experiments are implemented to illustrate the convergence and computational performance of our a...

In this study, a sampled-data nonlinear model predictive control scheme is developed. The control algorithm uses a prediction horizon with variable length, a terminal constraint set, and a feedback controller defined on this set. Following a suboptimal solution strategy, a defined number of steps of an iterative optimisation routine improve the current input trajectory at each sampling point. The value of the objective function monotonically decreases and the state converges to a target set. A discrete-time formulation of the algorithm and a discrete-time design model ensure high computational efficiency and avoid an ad hoc quasi-continuous implementation. This design technique for a fast sampled-data nonlinear model predictive control algorithm is the main contribution of the paper. Based on a benchmark control problem, the performance of the developed control algorithm is assessed against state-of-the-art nonlinear model predictive control methods available in the literature. This assessment dem...

Multipopulation differential evolution combined with opposition-based learning is developed to improve the convergence efficiency and optimization accuracy for heat exchanger network synthesis. The algorithm is based on a stagewise superstructure simultaneous optimization model without considering stream splitting. The candidate population and its opposite population are searched in parallel. Mutation operations are implemented on both populations to provide a full information exchange among populations at each generation. A regrouping schedule is introduced to avoid premature convergence. The algorithm is applied to five heat exchanger network cases of different sizes. More economic networks are found using this method with less computational time.

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception - the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm.

This study presents a new trust-region algorithm to solve the l1-minimization problem with applications to compressed sensing (CS) and image deblurring that will be augmented with a shrinkage operation to produce a new iteration whenever an approximated solution of the trust-region subproblem lies within one and iterate is successful, simultaneously. Otherwise, a nonmonotone Armijo-type line search strategy incorporates with shrinkage technique, which includes a convex combination of the maximum function value of some preceding iterates and the current function value. Therefore, the proposed approach takes advantages of both the effective trust-region and nonmonotone Armijo-type line search with a shrinkage operation. It is believed that selecting an appropriate shrinkage parameter according to a new procedure can improve the efficiency of our algorithm. The global convergence and the R-linear convergence rate of the proposed approach are proved for which numerical results are also reported.

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.

In this paper, we present a nonsmooth trust region method for solving linearly constrained optimization problems with a locally Lipschitz objective function. Using the approximation of the steepest descent direction, a quadratic approximation of the objective function is constructed. The null space technique is applied to handle the constraints of the quadratic subproblem. Next, the CG-Steihaug method is applied to solve the new approximation quadratic model with only the trust region constraint. Finally, the convergence of presented algorithm is proved. This algorithm is implemented in the MATLAB environment and the numerical results are reported.

This study investigated the multi-target circumnavigation problem. The multi-target circumnavigation problems involve a group of agents circumnavigating moving targets in a coordinated fashion. To address the problem, a decentralised estimator is first constructed at each agent to estimate the geometric centre of the targets. Then, the distributed control strategy is developed by means of the estimator, which guarantees that the agents preserve the desired distance to the target centre and rotate around the targets at uniformly spaced angles. In particular, the topology structure of the agents only needs to be a tree rather than the ring. Thus, the control scheme is more feasible and robust and requires less information. The convergence of the proposed algorithms is demonstrated based on Lasalle's invariance principle and algebraic graph theory. Several numerical simulations are provided to validate the results.

In this paper, we propose the new extragradient algorithms for an α-inverse-strongly monotone operator and a relatively nonexpansive mapping in Banach spaces. We prove convergence theorems by this methods under suitable conditions. Applying our algorithms, we find a zero paint of maximal monotone operators. Using FMINCON optimization toolbox in MATLAB, we give an example to illustrate the usability of our results.

A new methodology for the implementation of high resolution (HR) scheme is being presented. The proposed method is a revision of the existing normalized weighting factor (NWF) method and henceforth, it is termed as revised normalized weighting factor (RNWF) method. Unlike the previous method which is penta-diagonal in nature, the RNWF method generates tri-diagonal system of linear equations and is expected to be computationally inexpensive and robust to use. This method relies on the normalized weighting factors for its formulation in which implicit terms are formed based on the contribution of neighbouring grid points and explicit source terms are formed based on the contribution of far-off grid points of the control volume. Moreover, proper NWF are proposed for the downwind line of the Normalized Variable Diagram (NVD). Further to assess the performance of this method, iterations required for the convergence of HR schemes and to configure the CPU clock time, pure advection tests (viz. Step, Double-Step ...

The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each player’s strategy set depends on the rivals’ strategy set. In this paper, we presented a half-space projection method for solving the quasi-variational inequality problem which is a formulation of the GNEP. The difference from the known projection methods is due to the next iterate point in this method is obtained by directly projecting a point onto a half-space. Thus, our next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. Compared with the known methods, this method can reduce one projection of a vector onto the strategy set per iteration. Numerical results show that this method not only outperforms the known method but is also less dependent on the initial value than the known method.

This technical note addresses the new nonlinear protocol class of doubly stochastic quadratic operators (DSQOs) for coordination of consensus problem in multi-agent systems (MAS). We derive the conditions for ensuring that every agent reaches consensus on a desired rate of the group's decision where the group decision value in its agent's initial statuses varies. Besides that, we investigate a nonlinear protocol sub-class of extreme DSQO (EDSQO) to reach a consensus for MAS to a common value with nonlinear low-complexity rules and fast time convergence if the interactions for each agent are not selfish. In addition, to extend the results to reach a consensus and to avoid the selfish case we specify a general class of DSQO for reaching a consensus under any given case of initial states. The case that MAS reach a consensus by DSQO is if each member of the agent group has positive interactions of DSQO (PDSQO) with the others. The convergence of both EDSQO and PDSQO classes is found to be directed tow...

The stability of a prediction-based controller for linear time-invariant (LTI) systems is studied in the presence of time-varying input and output delays. The uncertain delay case is treated as well as the partial state knowledge case. The reduction method is used in order to prove the convergence of the closed-loop system including the state observer, the predictor and the plant. Explicit conditions that guarantee the closed-loop stability are given, thanks to a Lyapunov-Razumikhin analysis. Simulations illustrate the theoretical results.