We consider a variational inequality problem, where the cost mapping is the sum of a single-valued mapping and the subdifferential mapping of a convex function. For this problem we introduce a new class of equivalent optimization formulations; based on them, we also provide the first convergence analysis of descent algorithms for the problem. The optimization formulations constitute generalizat...

For getting the numerical solution of linear complementary problem (LCP), there are many methods such as modulus-based matrix splitting iteration and nonsmooth Newton?s method. We proposed Square-Newton method to solve LCP. This could LCP efficiently. gave theoretical analysis experiments in paper.

We consider a polyhedron intersected by a two-term disjunction, and we characterize the polyhedron resulting from taking its closed convex hull. This generalizes an earlier result of Conforti, Wolsey and Zambelli on split disjunctions. We also recover as a special case the valid inequalities derived by Judice, Sherali, Ribeiro and Faustino for linear complementarity problems.

We define a new fundamental constant associated with a P-matrix and show that this constant has various useful properties for the P-matrix linear complementarity problems (LCP). In particular, this constant is sharper than the Mathias-Pang constant in deriving perturbation bounds for the P-matrix LCP. Moreover, this new constant defines a measure of sensitivity of the solution of the P-matrix L...

New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a "best" error bound emerges from our comparisons as the sum of two natural residuals.

The paper establishes a computational encIosure of the solution of the linear complementarity problem (q, M), where M is assumed to be an H-matrix with a positive main diagonal. A dass of problems with interval data, which can arise in approximating the solutions of free boundary problems, is also treated successfully.

Although the general linear complementarity problem (LCP) is NP-complete, there are special classes that can be solved in polynomial time. One example is the type where the defining matrix is nondegenerate and for which the n-step property holds. In this paper we consider an extension of the property to the degenerate case by introducing the concept of an extended n-step vector and matrix. It i...