Abstract:

We studied the following nonlinear complementarity problem: f: Rⁿ→Rⁿ, find [WTHX]x[WT]≥0, such that f(x)≥0, x^Tf(x)=0. We used PoineareBohn’s homotopy invariance theorem of degree to derive an alternative theorem. Based on this result, a sufficiently condition was established to assure the existence and boundedness of solution curve, when f is a monotone map, quasimonotone map, P^*-map, quasi-P^*-map.

Key words: complementarity problems, monotone map, quasimonotone map, P^*-map, quasi-P^*-map