We present a first-order quadratic cone programming algorithm that can scale to very large problem sizes and produce modest accuracy solutions quickly. Our returns primal-dual optimal when available or certificates of infeasibility otherwise. It is derived by applying Douglas--Rachford splitting homogeneous embedding the linear complementarity problem, which general set membership includes prog...

Abstract We study a predictor-corrector interior-point algorithm for solving general linear complementarity problems from the implementation point of view. analyze method proposed by Illés, Nagy and Terlaky [1] that extends published Potra Liu [2] to problems. A new determining step size corrector direction is presented. Using code implemented in C++ programming language, we can solve large-sca...

For the nonlinear complementarity problem we derive norm bounds for the error of an approximate solution, generalizing the known results for the linear case. Furthermore, we present a linear system with interval data, whose solution set contains the error of an approximate solution. We perform extensive numerical tests and compare the different approaches.

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...