Multiple-objective approximation of feasible but unsolvable linear complementarity problems

Using a multiple-objective framework, feasible linear complementarity problems (LCPs) are handled in a unified manner. The resulting procedure either solves the feasible LCP or, under certain conditions, produces an approximate solution which is an efficient point of the associated multiple-objective problem. A mathematical existence theory is developed which allows both specialization and extension of earlier results in multiple-obkective programming. Two perturbation approaches to finding the closest solvable LCPs to a given unsolvable LCP are proposed. Several illustrative examples are provided and discussed.