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Abstract: The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms. [Copyright &y& Elsevier]

Abstract: Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asian options are related through an equation. The discretely monitored version is usually found in practice instead of the continuously monitored version usually encountered in the literature. This paper presents the first provably quadratic-time convergent lattice algorithm for pricing fixed-strike European-style discretely monitored Asian options. It is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose the number of states for each node of the lattice. Extensive numerical experiments and comparisons with many existing numerical methods confirm the performance claims and the competitiveness of our algorithm. This result places fixed-strike European-style discretely monitored Asian options in the same complexity class as vanilla options. [Copyright &y& Elsevier]

Abstract: In this paper, a heuristic algorithm, different from the Frank–Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, the new method need not enumerate initially all feasible paths for all origin/destination (O/D) pairs, but can give all paths used between each O/D pair and the path flows accordingly while the new algorithm obtains an optimal traffic assignment. Some convergence issues of the new method is discussed in this paper. Numerical experiments show that the new method is efficient and robust. [Copyright &y& Elsevier]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In the CQ-like algorithms for the split feasibility problem, in order to get the step-size, one has to compute the largest eigenvalue of the related matrix or use some line search scheme. Our contribution in this short note is to give a simple CQ-like algorithm in which the step-size is directly computed. The algorithm presented in this paper not only need not to compute the largest eigenvalue of the related matrix but also need not to use any line search scheme. The theoretical convergence and numerical results are also given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, based on a symmetrically perturbed smoothing Fischer–Burmeister function, a non-interior continuation method is proposed for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. Under monotonicity, it is shown that our algorithm is globally and locally superlinearly convergent without requiring strict complementarity assumption at the SOCCP solution. Furthermore, the proposed algorithm has local quadratic convergence under mild conditions. Some numerical results are reported which indicate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper deals with the null controllability of an initial-boundary value problem for a parabolic coupled system with nonlinear terms of local and nonlocal kinds. The control is distributed in space and time and is exerted through one scalar function whose support can be arbitrarily small. We first prove that, if the initial data are sufficiently small and the linearized system at zero satisfies an appropriate coupling condition, the equations can be driven exactly to zero. We also present an iterative algorithm of the quasi-Newton kind for the computation of the control and we prove a convergence result. The behavior of this algorithm is illustrated with some numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the convergence of the double-shift and multi-shift QR algorithms for symmetric tridiagonal matrices. We analyze how to choose multi-shifts by comparing the relationships between the number of iterations, CPU time and the number of multi-shifts. Numerical tests and figures are performed. [Copyright &y& Elsevier]

Abstract: In this paper, a trust-region sequential quadratic programming algorithm with a modified filter acceptance mechanism is proposed for nonlinear equality constrained optimization. The most important advantage of the proposed algorithm is its avoidance of any feasibility restoration phase, a necessity in traditional filter methods. We solve quadratic programming subproblems based on the well-known Byrd–Omojokun trust-region method. Inexact solutions to these subproblems are allowed. Under some standard assumptions, global convergence of the proposed algorithm is established. Numerical results show our approach is potentially useful. [Copyright &y& Elsevier]

Abstract: An adaptive parameter tuning of particle swarm optimization based on velocity information (APSO-VI) algorithm is proposed. In this paper the velocity convergence of particles is first analyzed and the relationship between the velocity of particle and the search failures is pointed out, which reveals the reasons why PSO has relative poor global searching ability. Then this algorithm introduces the velocity information which is defined as the average absolute value of velocity of all the particles. A new strategy is presented that the inertia weight is dynamically adjusted according to average absolute value of velocity which follows a given nonlinear ideal velocity by feedback control, which can avoid the velocity closed to zero at the early stage. Under the guide of the nonlinear ideal velocity, APSO-VI can maintain appropriate swarm diversity and alleviate the premature convergence validly. Numerical experiments are conducted to compare the proposed algorithm with different variants of PSO on some benchmark functions. Experimental results show that the proposed algorithm remarkably improves the ability of PSO to jump out of the local optima and significantly enhance the convergence speed and precision. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a compact alternating direction implicit (ADI) scheme for solving the two-dimensional parabolic equation. The maximum norm convergence is proven, and the convergence rate is second-order in time and fourth-order in space. We develop a Richardson extrapolation algorithm to increase the accuracy to sixth-order both in time and space. Numerical experiments show the effectiveness of the method. [Copyright &y& Elsevier]

Abstract: The split feasibility problem is to find with , if such points exist, where A is a given real matrix, C and Q are nonempty closed convex sets in and , respectively. Byrne (2002) [2] proposed a well-known CQ algorithm for solving this problem. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively, and performs an additional projection step onto some simple closed convex set in each iteration. We further give a relaxation scheme for this modification to make it more easily implemented. Convergence results of both algorithms are analyzed, and preliminary numerical results are reported. We also extend these modified algorithms to solve the multiple-sets split feasibility problem, which is to find a point closest to the intersection of a family of closed convex sets in one space such that its image under a linear transformation will be closest to the intersection of another family of closed convex sets in the image space. [Copyright &y& Elsevier]

Abstract: In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new penalty-free-type method for nonlinear equality constrained problems. The new algorithm uses trust region framework and feasibility safeguarding technique. Moreover, it has no choice of penalty parameter and penalty function as a merit function, and it does not use the filter technique to avoid the penalty function either. We analyze the global convergence of the main algorithm under the standard assumptions. The preliminary numerical tests are reported. [Copyright &y& Elsevier]

Abstract: This paper considers Nyström type methods for solving a generalized aerofoil equation with weakly singular kernel. Based on sigmoidal transformations and Nyström method, we obtain new algorithms for solving this equation. Convergence analysis for this methods are given. Finally, numerical examples complete this work. [Copyright &y& Elsevier]

Abstract: Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the linear diffusion–reaction problem are derived. The convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion–reaction equations with these non classical conditions. [Copyright &y& Elsevier]

Abstract: This paper describes a numerical approximation to the solution of Volterra integral equations of the second kind. This algorithm combines trapezoidal and Simpson rules. We prove the convergence of the method. Numerical examples are provided to illustrate the accuracy of the method. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel hybrid immune algorithm (HIA) that can overcome the typical drawback of the artificial immune algorithm (AIA), which runs slowly and experiences slow convergence. The HIA combines the adaptive AIA based on the steepest descent algorithm. The HIA fully displays global search ability and the global convergence of the immune algorithm. At the same time, it inserts a quasi-descent operator to strengthen its local search ability. A good convergence of the HIA with the quasi-descent idea is shown as well. Numerical experiment results show that the HIA successfully improves running speed and convergence performance. [Copyright &y& Elsevier]

Abstract: This paper deals with fixed points methods related to the general class of demicontractive mappings (including the well-known classes of nonexpansive and quasi-nonexpansive mappings) in Hilbert spaces. Specifically, we point out some historical aspects concerning the concept of demicontactivity and we investigate a regularized variant of the Krasnoselski-Mann iteration that can be alternatively regarded as a simplified form of the inertial iteration (P-E. Maingé, J. Math. Anal. Appl. 344 (2008) 876–887) with non-constant relaxation factors. These two methods ensure the strong convergence of the generated sequence towards the least norm element of the set of fixed-points of demicontractive mappings. However, for convergence, our method does not require anymore the knowledge of some constant related to the involved demicontractive operator. A new and simpler proof is also proposed for its convergence even when involving non-constant relaxation factors. We point out the simplicity of this algorithm (at least from computational point of view) in comparison with other existing methods. We also present some numerical experiments concerning a convex feasibility problem, experiments that emphasize the characteristics of the considered algorithm comparing with a classical cyclic projection-type iteration. [Copyright &y& Elsevier]

Abstract: This paper is concerned with iterative solutions to a class of complex matrix equations, which include some previously investigated matrix equations as special cases. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of matrix equations. A sufficient condition is presented to guarantee that the proposed algorithm is convergent for an arbitrary initial matrix with a real representation of a complex matrix as tools. By using some properties of the real representation, a convergence condition that is easier to compute is also given in terms of original coefficient matrices. A numerical example is employed to illustrate the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper, the issue of multi-degree reduction of Bézier curves with C 1 and G 2-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method. [Copyright &y& Elsevier]

Abstract: This paper proposes a line search filter reduced Hessian method for nonlinear equality constrained optimization. The feature of the presented algorithm is that the reduced Hessian method is used to produce a search direction, a backtracking line search procedure to generate step size, some filtered rules to determine step acceptance, second order correction technique to reduce infeasibility and overcome the Maratos effects. It is shown that this algorithm does not suffer from the Maratos effects by using second order correction step, and under mild assumptions fast convergence to second order sufficient local solutions is achieved. The numerical experiment is reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, differential transform method (DTM), which is one of the approximate methods is implemented for solving the nonlinear Hirota–Satsuma coupled KdV partial differential equation. A variety of initial value system is considered, and the convergence of the method as applied to the Hirota–Satsuma coupled KdV equation is illustrated numerically. The obtained results are presented and only few terms of the expansion are required to obtain the approximate solution which is found to be accurate and efficient. Numerical examples are illustrated the pertinent features of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: Many real life problems can be stated as a minimax optimization problem, such as the problems in economics, finance, management, engineering and other fields. In this paper, we present an algorithm with nonmonotone strategy and second-order correction technique for minimax optimization problems. Using this scheme, the new algorithm can overcome the difficulties of the Maratos effect occurred in the nonsmooth optimization, and the global and superlinear convergence of the algorithm can be achieved accordingly. Numerical experiments indicate some advantages of this scheme. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to incorporate the preconditioned gradient path in a nonmonotone stabilization algorithm for unconstrained optimization. The global convergence and locally superlinear convergence are established for this class of algorithms. Finally, we report in details the numerical results which show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with iterative solutions to a class of complex matrix equations. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of complex matrix equations. The range of the convergence factor is given to guarantee that the proposed algorithm is convergent for arbitrary initial matrix by applying a real representation of a complex matrix as a tool. By using some properties of the real representation, a sufficient convergence condition that is easier to compute is also given by original coefficient matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an efficient branch and bound algorithm for globally solving sum of geometric fractional functions under geometric constraints, which arise in various practical problems. By using an equivalent transformation and a new linear relaxation technique, a linear relaxation programming problem of the equivalent problem is obtained. The proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems. Numerical results are reported to show the feasibility of our algorithm. [Copyright &y& Elsevier]

Abstract: In the paper, a new alternating-direction iterative method is proposed based on matrix splittings for solving saddle point problems. The convergence analysis for the new method is given. When the better values of parameters are employed, the proposed method has faster convergence rate and less time cost than the Uzawa algorithm with the optimal parameter and the Hermitian and skew-Hermitian splitting iterative method. Numerical examples further show the effectiveness of the method. [Copyright &y& Elsevier]

Abstract: This paper focuses on the computation issue of portfolio optimization with scenario-based CVaR. According to the semismoothness of the studied models, a smoothing technology is considered, and a smoothing SQP algorithm then is presented. The global convergence of the algorithm is established. Numerical examples arising from the allocation of generation assets in power markets are done. The computation efficiency between the proposed method and the linear programming (LP) method is compared. Numerical results show that the performance of the new approach is very good. The remarkable characteristic of the new method is threefold. First, the dimension of smoothing models for portfolio optimization with scenario-based CVaR is low and is independent of the number of samples. Second, the smoothing models retain the convexity of original portfolio optimization problems. Third, the complicated smoothing model that maximizes the profit under the CVaR constraint can be reduced to an ordinary optimization model equivalently. All of these show the advantage of the new method to improve the computation efficiency for solving portfolio optimization problems with CVaR measure. [Copyright &y& Elsevier]

Abstract: In this paper, a new descent algorithm for solving unconstrained optimization problem is presented. Its search direction is descent and line search procedure can be avoided except for the first iteration. It is globally convergent under mild conditions. The search direction of the new algorithm is generalized and convergence of corresponding algorithm is also proved. Numerical results show that the algorithm is efficient for given test problems. [Copyright &y& Elsevier]

Abstract: Based on the discretization methods for solving semi-infinite programming problems, this paper presents a new nonmonotonic trust region algorithm for a class of semi-infinite minimax programming problem. Under some mild assumptions, the global convergence of the proposed algorithm is given. Numerical tests are reported that show the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints. We shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new convergence rate for both symmetric and nonsymmetric positive definite problems. In our theory, “regularity and approximation” assumption is used. A new rate of convergence estimate with is used where α is a “regularity and approximation” parameter. Also, a new convergence rate is given by two-grid schemes. [Copyright &y& Elsevier]

Abstract: In this paper extended algorithm of Karmarkar’s interior point algorithm is considered. Theoretical aspects of the new algorithm are discussed. We show that the new iterative algorithm converges faster than former Karmarkar’s algorithms. Successful convergence for problems of different sizes is obtained. Numerical results show that when we use a new parameter in the classical Karmarkar’s algorithm, number of iterations is less than the number of iterations for two mentioned methods. [Copyright &y& Elsevier]

Abstract: In this paper, we study the convergence of the generalized accelerated overrelaxation (GAOR) iterative method. That is an extension of the classical convergence result of the generalized successive overrelaxation (GSOR) iterative method. We proposed some theorems, which they obtain better results than similar works. By some numerical examples we show the goodness of our results. [Copyright &y& Elsevier]