Recently Tseng (Math Program 83:159–185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204–225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related pro...

QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on the NE/SQP method of Pang and Gabriell14], this algorithm represents a signiicant advance in robustness at no cost in eeciency. In particular, the algorithm is shown to solve any solvable Lipschitz continuous, continuously diierentiable, pseudo-...

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...

We discuss local convergence of Newton’s method to a singular solution x∗ of the nonlinear equations F (x) = 0, for F : IR → IR. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution x∗ from a starlike domain around x∗ for F twice Lipschitz continuously differentiable and x∗ satisfying a particular regularity condition, can be adapted to the case i...

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...

We show that the problem of finding optimal strategies for both players in a simple stochastic game reduces to the generalized linear complementarity problem (GLCP) with a P-matrix, a well-studied problem whose hardness would imply NP = co-NP. This makes the rich GLCP theory and numerous existing algorithms available for simple stochastic games. As a special case, we get a reduction from binary...