On the Number of Solutions to a Class of Complementarity Problems

摘要

In this paper the problem of establishing the number of solutions to the complementarity problem is considered. For the case when the Jacobian of the mapping has all principal minors negative, and satisfies a condition at infinity, it is proved that the problem has either 0,1,2 or 3 solutions. It is shown that when the Jacobian has all principal minors positive, and satisfies a condition at infinity, the problem has a unique solution. The problem of solving nonlinear programs, certain nonlinear n person noncooperative games, general equilibrium models with linear production and several others can be stated as a complementarity problem on a closed convex and polyhedral cone.