In this paper, the concept of the strongly monotone type mapping is introduced, which contains the strongly monotone mapping and firmly type nonexpansive mapping as special cases. We show the equivalence between the fixed point problem and the complementarity problem of strongly monotone type mapping. Furthermore, it is obtained that an iteration sequence strongly converges to a unique solution...

In this article, we propose a new merit function based on sub-additive functions for solving a nonlinear complementarity problem (NCP). This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (DC) program and we can therefore use DC Algorithm to locally solve it. We prove that in the case of a...

In this paper, we propose primal-dual potential-reduction algorithms which can start from an infeasible interior point. We rst describe two such algorithms and show that both are polynomial-time bounded. One of the algorithms decreases the Tanabe-Todd-Ye primal-dual potential function by a constant at each iteration under the condition that the duality gap decreases by at most the same ratio as...

We present an infeasible-interior-point algorithm for monotone linear complementarity problems in which the search directions are affine scaling directions and the step lengths are obtained from simple formulae that ensure both global and superlinear convergence. By choosing the value of a parameter in appropriate ways, polynomial complexity and convergence with Q-order up to (but not including...

The fixed point problem of piecewise constant mappings in Rn is investigated. This a polyhedral complementarity problem, which generalization the linear problem. Such arose author?s research on economic equilibrium exchange models, where were considered price simplex. author proposed an original approach complementarity, made it possible to obtain simple algorithms for solving present study met...

Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation|one that has fewer constraints than the \stan-dard" QP formulation|is available. We mention several instances of this class, including the known case in which the coeecient matrix in the LCP...

In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not de...

In this paper we construct a regularization Newton method for solving the nonlinear complementarity problem (NCP(F)) and analyze its convergence properties under the assumption that F is a P0-function. We prove that every accumulation point of the sequence of iterates is a solution of NCP(F) and that the sequence of iterates is bounded if the solution set of NCP(F) is nonempty and bounded. More...