求解非单调变分不等式的一种半空间投影算法

A HALF-SPACE PROJECTION ALGORITHM FOR SOLVING VARIATIONAL INEQUALITIES WITHOUT MONOTONICITY

本文提出了一种求解非单调变分不等式的半空间投影算法,在映射是连续和对偶变分不等式解集非空的假设条件下证明了该算法生成的无穷序列是全局收敛的,并在局部误差界和Lipschitz连续条件下给出了收敛率分析.通过数值实验验证了所提出算法的有效性和可行性.

In this paper,we present a half-space projection algorithm for solving nonmonotone variational inequalities.Under the assumption that the underlying mapping is continuous and the solution set of its dual variational inequality is nonempty,we prove that the infinite sequence generated by the algorithm is globally convergent,and establish the convergence rate analysis under local error and Lipschitz conditions.The effectiveness and feasibility of the proposed algorithm are proved by numerical experiments.