一种新修正的求解变分不等式的双次梯度外梯度算法

A New Modified Two-Subgradient Extragradient Algorithm for Solving Variational Inequality Problems

中文关键词:  双次梯度外梯度算法  单调  Lipschitz连续  变分不等式  Hilbert空间

英文关键词:two-subgradient extragradient algorithm  monotone  Lipschitz continuous  variational inequality  Hilbert space

中文摘要:

      当可行集为一光滑凸函数的下水平集时, 本文提出一种修正的双次梯度外梯度算法(MTSEGA)用于求解Hilbert空间中单调且Lipschitz连续的变分不等式. MTSEGA在每步迭代过程中仅需计算向半空间的两次投影及一次映射的值. 在与已知算法相同的假设条件下, 证明了新算法产生的序列能弱收敛到相关问题的一个解.

英文摘要:

      In this paper, we propose a modified two-subgradient extragradient algorithm (MTSEGA) for solving monotone and Lipschitz continuous variational inequalities with the feasible set being a level set of a smooth convex function in Hilbert space. The advantage of MTSEGA is that all the projections are computed onto a half-space per iteration. Moreover, MTSEGA only needs one computation of the underlying mapping per iteration. Under the same assumptions with the known algorithm, we show that the sequence generated by this algorithm is weakly convergent to a solution of the concerned problem.