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Abstract: In this paper, we introduce a new and interesting system of generalized mixed quasi-variational-like inclusions with -accretive operators and relaxed cocoercive mappings which contains variational inequalities, variational inclusions, systems of variational inequalities, systems of variational-like inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the -accretive operators, we prove the existence of solutions and the convergence of a new -step iterative algorithm for this system of generalized mixed quasi-variational-like inclusions in real -uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature. [Copyright &y& Elsevier]

In this paper, we discuss the convergence of the DFP algorithm with revised search direction. Under some inexact line searches, we prove that the algorithm is globally convergent for continuously differentiable functions and the rate of convergence of the algorithm is one-step superlinear and n-step second order for uniformly convex objective functions.From the proof of this paper, we obtain the superlinear and n-step second-order convergence of the DFP algorithm for uniformly convex objective functions. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a FEM and two-grid FEM decoupling algorithms for elliptic problems on disjoint domains. First, we study the rate of convergence of the FEM and, in particular, we obtain a superconvergence result. Then with proposed algorithms, the solution of the multi-component domain problem (simple example — two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms. [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: In this paper we propose an iterative method to calculate the largest eigenvalue of a nonnegative tensor. We prove this method converges for any irreducible nonnegative tensor. We also apply this method to study the positive definiteness of a multivariate form. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and study a new class of variational inclusions in Banach spaces. For solving such class of variational inclusions, we introduce a new notion of -monotone operator and prove the Lipschitz continuity of the proximal mapping associated with the -monotone operator. By using the proximal mapping, an iterative algorithm for solving such class of variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of iterative sequence generated by the algorithm. [Copyright &y& Elsevier]

Abstract: In general, proofs of convergence and stability are difficult for symplectic schemes of nonlinear equations. In this paper, a symplectic difference scheme is proposed for an initial-boundary value problem of a coupled nonlinear Schrödinger system. An important lemma and an induction argument are used to prove the unique solvability, convergence and stability of numerical solutions. An iterative algorithm is also proposed for the symplectic scheme and its convergence is proved. Numerical examples show the efficiency of the symplectic scheme and the correction of our numerical analysis. [Copyright &y& Elsevier]

Abstract: This paper considers the nonlinearly constrained continuous global minimization problem. Based on the idea of the penalty function method, an auxiliary function, which has approximately the same global minimizers as the original problem, is constructed. An algorithm is developed to minimize the auxiliary function to find an approximate constrained global minimizer of the constrained global minimization problem. The algorithm can escape from the previously converged local minimizers, and can converge to an approximate global minimizer of the problem asymptotically with probability one. Numerical experiments show that it is better than some other well known recent methods for constrained global minimization problems. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a kind of QP-free feasible algorithm which solves an inequality constrained nonlinear optimization problem. Under some weaker conditions than those in [H. Qi, L. Qi, A New QP-free, globally convergent, locally superlinear convergent algorithm for inequality constrained optimization, SIAM J. Optim. 11 (2000) 113–132], we prove that the algorithm is implementable and globally convergent. Moreover, some numerical test results are given to indicate that the algorithm is quite promising. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the box constrained nonlinear integer programming problem. We present an auxiliary function, which has the same discrete global minimizers as the problem. The minimization of the function using a discrete local search method can escape successfully from previously converged discrete local minimizers by taking increasing values of a parameter. We propose an algorithm to find a global minimizer of the box constrained nonlinear integer programming problem. The algorithm minimizes the auxiliary function from random initial points. We prove that the algorithm can converge asymptotically with probability one. Numerical experiments on a set of test problems show that the algorithm is efficient and robust. [Copyright &y& Elsevier]

Abstract: In this paper, a new concept of -proximal mapping for a proper subdifferentiable functional (which may not be convex) on a Banach space is introduced. An existence and Lipschitz continuity of the -proximal mapping are proved. By using properties of the -proximal mapping, a new class of general mixed variational inequalities is introduced and studied in Banach spaces. An existence theorem of solutions is established and a new iterative algorithm for solving the general mixed variational inequality is suggested. A convergence criteria of the iterative sequence generated by the new algorithm is also given. [Copyright &y& Elsevier]

In this paper, a new gradient-related algorithm for solving large-scale unconstrained optimization problems is proposed. The new algorithm is a kind of line search method. The basic idea is to choose a combination of the current gradient and some previous search directions as a new search direction and to find a step-size by using various inexact line searches. Using more information at the current iterative step may improve the performance of the algorithm. This motivates us to find some new gradient algorithms which may be more effective than standard conjugate gradient methods. Uniformly gradient-related conception is useful and it can be used to analyze global convergence of the new algorithm. The global convergence and linear convergence rate of the new algorithm are investigated under diverse weak conditions. Numerical experiments show that the new algorithm seems to converge more stably and is superior to other similar methods in many situations. [Copyright &y& Elsevier]