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In recent years, Differential Evolution (DE) has shown excellent performance in solving optimization problems over continuous space and has been widely used in many fields of science and engineering. How to avoid the local optimal solution and how to improve the convergence performance of DE are hotpot problems for many researchers. In this paper, an improved differential evolution algorithm based on dual-strategy (DSIDE) is proposed. The DSIDE algorithm has two strategies. (1) An enhanced mutation strategy based on "DE/rand/1," which takes into account the influence of reference individuals on mutation and has strong global exploration and convergence ability. (2) A novel adaptive strategy for scaling factor and crossover probability based on fitness value has a positive impact on population diversity. The DSIDE algorithm is verified with other seven state-of-the-art DE variants under 30 benchmark functions. Furthermore, Wilcoxon sign rank-sum test, Friedman test, and Kruskal–Wallis test are utilized to analyze the results. The experiment results show that the proposed DSIDE algorithm can significantly improve the global optimization performance. [ABSTRACT FROM AUTHOR]

This paper constructs a dynamic multiobjective location model; three objectives are considered: the first objective maximizes the total utility of relief supplies, the second objective minimizes the number of temporary facilities needed to operate, and the third objective maximizes the satisfaction for all demand points. We propose an improved NSGA-II to solve the optimization problem. The computational experiments are divided into two sections: In the first procedure, the numerical experiment is constructed by the classical functions ZDT1, ZDT2, and DTLZ2; the results show that the proposed algorithm generates the exact Pareto front, and the convergence and uniformity of the proposed algorithm are better than the NSGA-II and MOEA/D. In the second procedure, the simulation experiment is constructed by a case in emergency management; the results show that the proposed algorithm is more reasonable than the traditional algorithms NSGA-II and MOEA/D in terms of the three objectives. It is proved that the improved NSGA-II algorithm, which is proposed in this paper, has high precision application for the sudden disaster crisis and emergency management. [ABSTRACT FROM AUTHOR]

The bat algorithm (BA) is a recent heuristic optimization algorithm based on the echolocation behavior of bats. However, the bat algorithm tends to fall into local optima and its optimization results are unstable because of its low global exploration ability. To solve these problems, a novel bat algorithm based on an integration strategy (IBA) is proposed in this paper. Through the integration strategy, an appropriate operator is adaptively selected to perform global search, so that the global search ability of the IBA is improved. Furthermore, the IBA disturbs the local optimum through a linear combination of Gaussian functions with different variances to avoid becoming trapped in local optima. The IBA also updates the velocity equation with an adaptive weight to further balance the exploration and exploitation. Moreover, the global convergence of the IBA is proved based on the convergence criterion of a stochastic algorithm. The performance of the IBA is evaluated on CEC2013 benchmark functions and compared with that of the standard BA as well as several of its variants. The results show that the IBA is superior to other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of convolutive blind source separation in frequency domain and introduce a solution to the problem in an independent vector analysis (IVA) framework. IVA utilizes both the statistical independence of different sources in each frequency bin and the statistical dependence of the same source in different frequency bins. However, most of previous works impose orthogonality constraint on the rows of each separation matrix which may undermine the separation performance. In this work, we propose a nonorthogonal IVA algorithm based on decoupled relative Newton method. This proposed algorithm updates the separation matrices row by row, and unlike deflation separation algorithm, there is no separation error accumulation arising. Simulation results are provided to show the superior convergence behavior and separation performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We propose a derivative-free trust region algorithm with a nonmonotone filter technique for bound constrained optimization. The derivative-free strategy is applied for special minimization functions in which derivatives are not all available. A nonmonotone filter technique ensures not only the trust region feature but also the global convergence under reasonable assumptions. Numerical experiments demonstrate that the new algorithm is effective for bound constrained optimization. Locally, optimal parameters with respect to overall computational time on a set of test problems are identified. The performance of the best choice of parameter values obtained by the algorithm we presented which differs from traditionally used values indicates that the algorithm proposed in this paper has a certain advantage for the nondifferentiable optimization problems. [ABSTRACT FROM AUTHOR]

Localization is one of the most important problems in wireless sensor networks. In this paper, we investigate the convergence rate estimate problem of a distributed localization algorithm which approximately formulates the localization problem as the convex feasibility problem including the consistent case and the inconsistent case. Although existing works established optimal consensus convergence analysis for this algorithm, they did not provide the convergence rate estimate. In this paper, we mainly show that for the consistent case the convergence rate of the optimal consensus will be exponential under some basic conditions, while for the inconsistent case we provide a necessary condition for the optimal consensus and a convergence rate estimate inequality. Furthermore, numerical examples are also provided to validate the established convergence and convergence rate results. [ABSTRACT FROM AUTHOR]

In this paper, we study and modify the algorithm of Kraikaew and Saejung for the class of total quasi-asymptotically nonexpansive case so that the strong convergence is guaranteed for the solution of split common fixed-point problems in Hilbert space. Moreover, we justify our result through an example. The results presented in this paper not only extend the result of Kraikaew and Saejung but also extend, improve, and generalize some existing results in the literature. [ABSTRACT FROM AUTHOR]

Plant Propagation Algorithms (PPA) are powerful and flexible solvers for optimisation problems. They are nature-inspired heuristics which can be applied to any optimisation/search problem. There is a growing body of research, mainly experimental, on PPA in the literature. Little, however, has been done on the theoretical front. Given the prominence this algorithm is gaining in terms of performance on benchmark problems as well as practical ones, some theoretical insight into its convergence is needed. The current paper is aimed at fulfilling this by providing a sketch for a global convergence analysis. [ABSTRACT FROM AUTHOR]

This paper gives a modified Hestenes and Stiefel (HS) conjugate gradient algorithm under the Yuan-Wei-Lu inexact line search technique for large-scale unconstrained optimization problems, where the proposed algorithm has the following properties: (1) the new search direction possesses not only a sufficient descent property but also a trust region feature; (2) the presented algorithm has global convergence for nonconvex functions; (3) the numerical experiment showed that the new algorithm is more effective than similar algorithms. [ABSTRACT FROM AUTHOR]

Substation locating and sizing is an important component of urban power networks. In this paper, an improved method based on the weighted Voronoi diagram and transportation model for substation planning is proposed, which can optimize the location, capacity, and power supply range for each substation with the minimuminvestment which contains the cost of the lines, substations, and annual operation expense. The weighted Voronoi diagram (WVD) whose weights can be adaptively adjusted can calculate the location and the capacity for each substation with good performance of global convergence and better convergence speed. Transportation model can simulate the best correspondence relationship between the loads and substations. The impact of geographical factors is also considered in this paper. Large amount of experiments show that the improved method can get more reasonable and more optimized planning result within shorter time than the original WVD and other algorithms. [ABSTRACT FROM AUTHOR]

Multi objective programming problems have been widely applied to various engineering areas which include optimal design of an automotive engine, economics, and military strategies. In this paper, we propose a noninterior path following algorithm to solve a class of multi objective programming problems. Under suitable conditions, a smooth path will be proven to exist. This can give a constructive proof of the existence of solutions and lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper. [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]

We introduce a new iterative algorithm for finding a common element of a fixed point problem of amenable semigroups of nonexpansive mappings, the set solutions of a system of a general system of generalized equilibria in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative algorithm to a common element of the above three sets under some suitable conditions. As applications, at the end of the paper, we apply our results to find the minimum-norm solutions which solve some quadratic minimization problems. The results obtained in this paper extend and improve many recent ones announced by many others. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a synthetic algorithm for tracking a moving object in a multiple-dynamic obstacles environment based on kinematically planar manipulators. By observing the motions of the object and obstacles, Spline filter associated with polynomial fitting is utilized to predict their moving paths for a period of time in the future. Several feasible paths for the manipulator in Cartesian space can be planned according to the predicted moving paths and the defined feasibility criterion. The shortest one among these feasible paths is selected as the optimized path. Then the real-time path along the optimized path is planned for the manipulator to track the moving object in real-time. To improve the convergence rate of tracking, a virtual controller based on PD controller is designed to adaptively adjust the real-time path. In the process of tracking, the null space of inverse kinematic and the local rotation coordinate method (LRCM) are utilized for the arms and the end-effector to avoid obstacles, respectively. Finally, the moving object in a multiple-dynamic obstacles environment is thus tracked via real-time updating the joint angles of manipulator according to the iterative method. Simulation results show that the proposed algorithm is feasible to track a moving object in a multiple-dynamic obstacles environment. [ABSTRACT FROM AUTHOR]

In this paper, we present two different relaxed gradient based iterative (RGI) algorithms for solving the symmetric and skew symmetric solution of the Sylvester matrix equation AX+XB=C. By using these two iterative methods, it is proved that the iterative solution converges to its true symmetric (skew symmetric) solution under some appropriate assumptions when any initial symmetric (skew symmetric) matrix X0 is taken. Finally, two numerical examples are given to illustrate that the introduced iterative algorithms are more efficient. [ABSTRACT FROM AUTHOR]

In this paper, we propose an extension of quasi-equilibriumproblems fromthe convex case to the nonconvex case and fromHilbert spaces to Banach spaces. The proposed problem is called quasi-variational problem. We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a novel implicit iterative algorithm for the split common fixed point problem for the demicontractive operators U, T, and  xn=αnfxn+1-αnUλxn-ρnA*I-TAxn, n≥0, where Uλ=(1-λ)I+λU, and we obtain the sequence which strongly converges to a solution x^ of this problem, and the solution x^ satisfies the variational inequality. 〈x^-f(x^),x^-z〉≤0, ∀z∈S, where S denotes the set of all solutions of the split common fixed point problem. [ABSTRACT FROM AUTHOR]

Due to its fast convergence and population-based nature, particle swarm optimization (PSO) has been widely applied to address the multiobjective optimization problems (MOPs). However, the classical PSO has been proved to be not a global search algorithm. Therefore, there may exist the problem of not being able to converge to global optima in the multiobjective PSO-based algorithms. In this paper, making full use of the global convergence property of quantum-behaved particle swarm optimization (QPSO), a novel multiobjective QPSO algorithm based on the ring model is proposed. Based on the ring model, the position-update strategy is improved to address MOPs. The employment of a novel communication mechanism between particles effectively slows down the descent speed of the swarm diversity. Moreover, the searching ability is further improved by adjusting the position of local attractor. Experiment results show that the proposed algorithm is highly competitive on both convergence and diversity in solving the MOPs. In addition, the advantage becomes even more obvious with the number of objectives increasing. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence and convergence analysis of the solutions of the system of mixed variational inequalities in Banach spaces by using the generalized f projection operator. The results presented in this paper improve and extend important recent results of Zhang et al. (2011) and Wu and Huang (2007) and some recent results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A + M2)−1(0) and (B + M1)−1(0), where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. The results obtained in this paper extend and improve the corresponding results of Qin et al. 2011 from Hilbert spaces to Banach spaces and Petrot et al. 2011. Moreover, we also apply our results to some applications for solving convex feasibility problems. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is first to introduce the concept of total asymptotically nonexpansive mappings and to prove a Δ-convergence theorem for finding a common fixed point of the total asymptotically nonexpansive mappings and the asymptotically nonexpansive mappings. The demiclosed principle for this kind of mappings in CAT(0) space is also proved in the paper. Our results extend and improve many results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a strong convergence of a new parallel iterative algorithm with mean errors to a common fixed point for two finite families of C'iric' quasi-contractive operators in normed spaces. The results presented in this paper generalize and improve the corresponding results of Berinde, Gu, Rafiq, Rhoades, and Zamfirescu. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the notion of weak relatively nonexpansive multivalued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces. The weak relatively nonexpansive multivalued mappings are more generalized than relatively nonexpansive multivalued mappings. In this paper, an example will be given which is a weak relatively nonexpansive multivalued mapping but not a relatively nonexpansive multivalued mapping. In order to get the strong convergence theorems for weak relatively nonexpansive multivalued mappings, a new monotone hybrid iteration algorithm with generalized (metric) projection is presented and is used to approximate the fixed point of weak relatively nonexpansive multivalued mappings. In this paper, the notion of multivalued resolvent of maximal monotone operator has been also presented which is a weak relatively nonexpansive multivalued mapping and can be used to find the zero point of maximal monotone operator. [ABSTRACT FROM AUTHOR]

Many applied problems such as image reconstructions and signal processing can be formulated as the split feasibility problem (SFP). Some algorithms have been introduced in the literature for solving the (SFP). In this paper, we will continue to consider the convergence analysis of the regularized methods for the (SFP). Two regularized methods are presented in the present paper. Under some different control conditions, we prove that the suggested algorithms strongly converge to the minimum norm solution of the (SFP). [ABSTRACT FROM AUTHOR]

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi-f- asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors. [ABSTRACT FROM AUTHOR]

This paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field. [ABSTRACT FROM AUTHOR]

Gas source localization (GSL) is a critical component in wireless sensor network (WSN) which can be used to estimate the position of gas leaks through the gas concentration measured by the monitoring nodes. In this paper, we first derive a gas diffusion model under windy conditions based on the gas diffusion theory. Because of the nonlinearity of the gas diffusion model under windy conditions, the traditional weighted centroid algorithm for gas source localization produces very inaccurate estimation of the source location. To address this problem, we propose a novel gas source localization algorithm which combines the weighted centroid method and particle filter. Simulation results validate the effectiveness of our algorithm under unknown gas source strength. Compared to weighted centroid method alone, our algorithm shows a higher accuracy in location. Moreover, its convergence rate is improved by the preestimation of initial value. [ABSTRACT FROM AUTHOR]

This paper proposes a twice rapid transfer alignment algorithm based on dual models in order to solve the problems such as long convergence time, poor accuracy, and heavy computation burden resulting from the traditional nonlinear error models. The quaternion matching method based on quaternion error model along with the extended Kalman filter (EKF) is applied to deal with the large misalignment in the first phase. Then in the second transfer alignment phase, velocity plus attitude matching method as well as classical Kalman filter is adopted. The simulation and the results of vehicle tests demonstrate that this method combines the advantages of both nonlinear and linear error models with the guarantee of accuracy and fastness. [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]

This paper proposes an improved Hopfield neural network (I-HNN) algorithm to optimize the slot assignment scheme in wireless sensor networks. The key advantage of the proposed algorithm is to increase the convergence probability under different traffic loads. To achieve this, nodes can adjust their slot demands according to the traffic load, slots number, and demand history. Various aspects of the network performances with the proposed I-HNN algorithm are evaluated via simulation. The results indicate that I-HNN is suitable for wireless sensor networks with dynamically varying traffic. In particular, it can increase the convergence probability and slot utilization under the heavy traffic load. [ABSTRACT FROM AUTHOR]

This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarmoptimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient. [ABSTRACT FROM AUTHOR]

We consider in this paper expansions of functions based on the rational orthogonal basis for the space of square integrable functions. The basis functions have nonnegative instantaneous frequencies so that the expansions make physical sense. We discuss the almost everywhere convergence of the expansions and develop a fast algorithm for computing the coefficients arising in the expansions by combining the characterization of the coefficients with the fast Fourier transform. [ABSTRACT FROM AUTHOR]

Satisfying consistency requirements of pairwise comparison matrix (PCM) is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP) or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts a segment tree to gradually approach the greatest lower bound of the distance with the original PCM to obtain the middle value of an adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value of an adjustable PCM based on two constraints. The experiments for crisp elements show that the proposed approach can preserve more of the original information than previous works of the same consistent value. The convergence rate of our algorithm is significantly faster than previous works with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs. [ABSTRACT FROM AUTHOR]

Two numerical integration rules based on composition of Gauss-Legendre formulas for solving integration of fuzzy numbers-valued functions are investigated in this paper. The methods' constructions are presented and the corresponding convergence theorems are shown in detail. Two numerical examples are given to illustrate the proposed algorithms finally. [ABSTRACT FROM AUTHOR]

This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem (P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of (P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of (P) does not exist, which can be seen as an accelerating device for the solution algorithm of (P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem (P) provided that the number of variables is not too large. [ABSTRACT FROM AUTHOR]

Many researches have identified that differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter algorithms for global optimization problems. However, a stagnation problem still exists in DE variants. In order to overcome the disadvantage, two improvement ideas have gradually appeared recently. One is to combine multiple mutation operators for balancing the exploration and exploitation ability. The other is to develop convergent DE variants in theory for decreasing the occurrence probability of the stagnation. Given that, this paper proposes a subspace clustering mutation operator, called SC qrtop. Five DE variants, which hold global convergence in probability, are then developed by combining the proposed operator and five mutation operators of DE, respectively. The SC qrtop randomly selects an elite individual as a perturbation's center and employs the difference between two randomly generated boundary individuals as a perturbation's step. Theoretical analyses and numerical simulations demonstrate that SC qrtop prefers to search in the orthogonal subspace centering on the elite individual. Experimental results on CEC2005 benchmark functions indicate that all five convergent DE variants with SC qrtop mutation outperform the corresponding DE algorithms. [ABSTRACT FROM AUTHOR]

Many improved differential Evolution (DE) algorithms have emerged as a very competitive class of evolutionary computation more than a decade ago. However, few improved DE algorithms guarantee global convergence in theory. This paper developed a convergent DE algorithmin theory, which employs a self-adaptation scheme for the parameters and two operators, that is, uniform mutation and hidden adaptation selection (haS) operators. The parameter self-adaptation and uniformmutation operator enhance the diversity of populations and guarantee ergodicity. The haS can automatically remove some inferior individuals in the process of the enhancing population diversity. The haS controls the proposed algorithm to break the loop of current generation with a small probability. The breaking probability is a hidden adaptation and proportional to the changes of the number of inferior individuals. The proposed algorithm is tested on ten engineering optimization problems taken from IEEE CEC2011. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem for multiagent systems with nonlinear dynamics and time delays. A distributed adaptive consensus protocol is proposed in which the time delays are explicitly included in the adaptive algorithm. It is shown that the resultant closed loop system involves doubly larger time delays, making the stability analysis nontrivial. Stability condition on maximum tolerable time delay is established and controlled by the proposed two-hop adaptive algorithm. The explicit expression of the delay margin is derived and analyzed in the frequency domain. Both the agent state errors and the estimation parameter errors converge to zero. A simulation example is illustrated to verify the theory results. [ABSTRACT FROM AUTHOR]

This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations A1XB1 + A2XB2 = F1 and C1XD1 + C2XD2 = F2. The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The nonlinear minimax problems without constraints are discussed. Due to the expensive computation for solving QP subproblems with inequality constraints of SQP algorithms, in this paper, a QP-free algorithm which is also called sequential systems of linear equations algorithm is presented. At each iteration, only two systems of linear equations with the same coefficient matrix need to be solved, and the dimension of each subproblem is not of full dimension. The proposed algorithm does not need any penalty parameters and barrier parameters, and it has small computation cost. In addition, the parameters in the proposed algorithm are few, and the stability of the algorithm is well. Convergence property is described and some numerical results are provided. [ABSTRACT FROM AUTHOR]

Many application problems of practical interest can be posed as structured convex optimization models. In this paper, we study a new first-order primaldual algorithm. The method can be easily implementable, provided that the resolvent operators of the component objective functions are simple to evaluate. We show that the proposed method can be interpreted as a proximal point algorithm with a customized metric proximal parameter. Convergence property is established under the analytic contraction framework. Finally, we verify the efficiency of the algorithm by solving the stable principal component pursuit problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show the strong convergence theorems of the CQ algorithm for H-monotone operators in Hilbert spaces by hybrid method in the mathematical programming. The main results extend and improve the corresponding results. Moreover, the assumption conditions of our results are weaker than those of the corresponding results. [ABSTRACT FROM AUTHOR]

An improved differential evolution (DE) method based on the dynamic search strategy (IDEBDSS) is proposed to solve dynamic economic dispatch problem with valve-point effects in this paper. The proposed method combines the DE algorithm with the dynamic search strategy, which improves the performance of the algorithm. DE is the main optimizer in the method proposed. While chaotic sequences are applied to obtain the dynamic parameter settings in DE, dynamic search strategy which consists of two steps, global search strategy and local search strategy, is used to improve algorithm efficiency. To accelerate convergence, a new infeasible solution handing method is adopted in the local search strategy; meanwhile, an orthogonal crossover (OX) operator is added to the global search strategy to enhance the optimization search ability. Finally, the feasibility and effectiveness of the proposed methods are demonstrated by three test systems, and the simulation results reveal that the IDEBDSS method can obtain better solutions with higher efficiency than the standard DE and other methods reported in the recent literature. [ABSTRACT FROM AUTHOR]

Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy lights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy "DE/best/2" in differential algorithm. Lévy lights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space. [ABSTRACT FROM AUTHOR]

The effectiveness of wireless sensor networks (WSN) depends on the regional coverage provided by node deployment, which is one of the key topics in WSN. Virtual force-based algorithms (VFA) are popular approaches for this problem. In VFA, all nodes are seen as points subject to repulsive and attractive force exerted among them and can move according to the calculated force. In this paper, a sensor deployment algorithm for mobile WSN based on van der Waals force is proposed. Friction force is introduced into the equation of force, the relationship of adjacency of nodes is defined by Delaunay triangulation, and the force calculated produce acceleration for nodes to move. An evaluation metric called pair correlation function is introduced here to evaluate the uniformity of the node distribution. Simulation results and comparisons have showed that the proposed approach has higher coverage rate, more uniformity in configuration, and moderate convergence time compared to some other virtual force algorithms. [ABSTRACT FROM AUTHOR]

A generalized gradient projection filter algorithm for inequality constrained optimization is presented. It has three merits. The first is that the amount of computation is lower, since the gradient matrix only needs to be computed one time at each iterate. The second is that the paper uses the filter technique instead of any penalty function for constrained programming. The third is that the algorithm is of global convergence and locally superlinear convergence under some mild conditions. [ABSTRACT FROM AUTHOR]

In the standard firefly algorithm, each firefly has the same step settings and its values decrease from iteration to iteration. Therefore, it may fall into the local optimum. Furthermore, the decreasing of step is restrained by the maximum of iteration, which has an influence on the convergence speed and precision. In order to avoid falling into the local optimum and reduce the impact of the maximum of iteration, a self-adaptive step firefly algorithm is proposed in the paper. Its core idea is setting the step of each firefly varying with the iteration, according to each firefly's historical information and current situation. Experiments are made to show the performance of our approach compared with the standard FA, based on sixteen standard testing benchmark functions. The results reveal that our method can prevent the premature convergence and improve the convergence speed and accurateness. [ABSTRACT FROM AUTHOR]

The generalized Nash equilibriumproblem(GNEP) is anextensionof the standard Nash equilibrium problem(NEP), inwhich each player's strategy set may depend on the rival player's strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation of the generalized Nash equilibrium using Nikaido-Isoda function as unconstrained optimization. We prove that our algorithms are globally convergent and the convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of the GNEP. [ABSTRACT FROM AUTHOR]