On Conditions for Strict Feasibility in Nonlinear Complementarity Problems

. The strict feasibility plays an important role in the development of theory and algorithms of complementarity problems. In this paper, we establish sufficient conditions to ensure the strict feasibility of a nonlinear complementarity problem. Our analytical method, based on a newly introduced concept of ¯-antifeasible sequence, can be viewed as a unified approach in proving the existence of a strictly feasible point. Some equivalent conditions of strict feasibility are also established for certain complementarity problems. Among others, we show that a P complementarity problem is strictly feasible if and only if its solution set is nonempty and bounded. This result extends a well-known result in monotone situation. Key words. Complementarity problems, strict feasibility, quasi-monotone maps, P 0 -maps, P -maps. AMS Subject Classifications: 90C30, 90C33 Abbreviated Title: Strict feasibility for NCP. 1 This work was partially supported by grant no. CUHK358/96P, Research Grants Cou..