求解拟变分不等式问题的一类无导数下降算法

A Derivative-free Descent Method for Solving Quasi-variational Inequality Problem

利用广义正则gap函数的方向导数,构造了一种迭代方向,提出了一类求解拟变分不等式问题的算法。此算法不需关心目标函数的梯度计算问题,与相关文献比较,该算法的适用范围更加广泛。在某些假设条件下,证明算法的收敛性。

Constructing a descent direction obtained from the directional differentiability of the （generalized） regularized gap function, we present a derivative--free descent method for solving the quasi--variational inequality problem in this paper. We do not need consider the gradient problem of the objection function. Compared with the ones in the related references, the method of this paper has the superiority that the application is more wider. Under some reasonable conditions, the convergence of the algorithm is proved.