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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: 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, 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: In this paper it is presented a compensated de Casteljau algorithm to accurately evaluate a bivariate polynomial in Bernstein–Bézier form. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. A forward error and a running error analysis are performed. Finally, some numerical experiments illustrate the accuracy of the proposed algorithm in ill-conditioned problems. [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: In this paper, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective. [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: In this paper, we propose an interval version of the generalized accelerated overrelaxation methods, which we refer to as IGAOR, for solving the linear complementarity problems, LCP (M, q), and develop a class of multisplitting IGAOR methods which can be easily implemented in parallel. In addition, in regards to the H-matrix with positive diagonal elements, we prove the convergence of these algorithms and illustrate their efficiency through our numerical results. [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: In this paper, we use the auxiliary principle technique in conjunction with the Bregman function to suggest and analyze a predictor–corrector method for solving invex equilibrium problems. We also study the convergence criteria of this new method under some mild conditions. We obtain, as special cases, new and known methods for solving variational-like inequalities and equilibrium problems. [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 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]