Homotopy Method for Variational Inequalities
徐庆, 于波, 冯果忱 · 数学进展 · 2001
Solving a finite-dimensional variational inequality is to find a vector x* ∈ X Rn such that where X is a nonempty, closed and convex subset of Rn and F is a mapping from Rn to itself,denoted by VI(X, F). The variational inequality problem (VIP) has had many successful practical applications in the last three decades. It has been used to formulate and investigate equilibrium models arising in economics, transportation, regional science and operations research. So far, a large number of existence conditions have been developed in the literature. Harker and Pang[1] gave excellent surveys of theories, methods and applications of VIPs.