Global Optimization Techniques for Mixed Complementarity Problems

Mixed quasi complementarity problems in topological vector spaces

In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solutio...

A box-constrained differentiable penalty method for nonlinear complementarity problems

Mathematical Programming Manuscript No. Feasible Descent Algorithms for Mixed Complementarity Problems

In this paper we consider a general algorithmic framework for solving nonlinear mixed complementarity problems. The main features of this framework are: (a) it is well-deened for an arbitrary mixed complementarity problem, (b) it generates only feasible iterates, (c) it has a strong global convergence theory, and (d) it is locally fast convergent under standard regularity assumptions. This fram...

Projected filter trust region methods for a semismooth least squares formulation of mixed complementarity problems

A reformulation of the mixed complementarity problem as a box constrained overdetermined system of semismooth equations or, equivalently, a box constrained nonlinear least squares problem with zero residual is presented. Based on this reformulation, a trust region method for the solution of mixed complementarity problems is considered. This trust region method contains elements from different a...

A Homotopy-Based Algorithm for Mixed Complementarity Problems

This paper develops an algorithm for solving mixed complementarity problems which is based upon probability one homotopy methods. After the complementarity problem is reformulated as a system of nonsmooth equations, a homotopy method is used to solve a sequence of smooth approximations to this system of equations. The global convergence properties of this approach are considerably stronger than...