Strict feasibility conditions in nonlinear complementarity problems

Strict feasibility plays an important role in the development of the theory and algorithms of complementarity problems. In this paper, we establish sufficient conditions to ensure strict feasibility of a nonlinear complementarity problem. Our analysis method, based on a newly introduced concept of μ-exceptional sequence, can be viewed as a unified approach for proving the existence of a strictly feasible point. Some equivalent conditions of strict feasibility are also developed for certain complementarity problems. In particular, we show that a P_*-complementarity problem is strictly feasible if and only if its solution set is nonempty and bounded.