Unified approaches for solvable and unsolvable linear complementarity problems

In this paper, general linear complementarity problems (LCPs) are studied via global optimization problems. In particular, unsolvable LCPs are reformulated as multicriteria optimization, minimax optimization and quadratic programming problems. The solvability and unsolvability of LCPs are obtained via these reformulations. Furthermore, first-order and second-order global optimality conditions of LCPs are derived. Some examples are also given to demonstrate these optimality conditions.Department of Applied Mathematic