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Abstract: This paper considers a stochastic mathematical program with hybrid equilibrium constraints (SMPHEC), which includes either “here-and-now” or “wait-and-see” type complementarity constraints. An example is given to describe the necessity to study SMPHEC. In order to solve the problem, the sampling average approximation techniques are employed to approximate the expectations and smoothing and penalty techniques are used to deal with the complementarity constraints. Limiting behaviors of the proposed approach are discussed. Preliminary numerical experiments show that the proposed approach is applicable. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new large-update primal–dual interior point algorithm for complementarity problems (CPs). Different from most interior point methods which are based on the logarithmic kernel function, the new method is based on a class of kernel functions ,, . We show that if a strictly feasible starting point is available and the undertaken problem satisfies some conditions, then the new large-update primal–dual interior point algorithm for CPs has iteration complexity which is currently the best known result for such methods with and . [Copyright &y& Elsevier]

Abstract: In this paper we consider the linear complementarity problem where the components of the input data M and q are not exactly known but can be enclosed in intervals. We compare three tests to each other each of which can be used by a computer that supports interval arithmetic to give guaranteed bounds for a solution of the LCP defined by M and q. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest and analyze a new modified proximal-point method for solving nonlinear complementarity problems. Under suitable conditions, we prove that the new method is globally convergent. We report some preliminary computational results to illustrate the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: The affine second-order cone complementarity problem (SOCCP) is a wide class of problems that contains the linear complementarity problem (LCP) as a special case. The purpose of this paper is to propose an iterative method for the symmetric affine SOCCP that is based on the idea of matrix splitting. Matrix-splitting methods have originally been developed for the solution of the system of linear equations and have subsequently been extended to the LCP and the affine variational inequality problem. In this paper, we first give conditions under which the matrix-splitting method converges to a solution of the affine SOCCP. We then present, as a particular realization of the matrix-splitting method, the block successive overrelaxation (SOR) method for the affine SOCCP involving a positive definite matrix, and propose an efficient method for solving subproblems. Finally, we report some numerical results with the proposed algorithm, where promising results are obtained especially for problems with sparse matrices. [Copyright &y& Elsevier]

Recent works have shown that a wide class of globally convergent interior point methods may manifest a weakness of convergence. Failures can be ascribed to the procedure of linesearch along the Newton step. In this paper, we introduce a globally convergent interior point method which performs backtracking along a piecewise linear path. Theoretical and computational results show the effectiveness of our proposal. [Copyright &y& Elsevier]