用于求解希尔伯特空间中变分不等式的次梯度外梯度法。
The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space.
作者信息
Censor Y, Gibali A, Reich S
机构信息
Department of Mathematics, University of Haifa, Mt. Carmel, 31905 Haifa, Israel.
出版信息
J Optim Theory Appl. 2011 Feb;148(2):318-335. doi: 10.1007/s10957-010-9757-3.
Abstract
We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.
摘要
我们提出了一种用于求解希尔伯特空间中变分不等式的次梯度外梯度方法。此外，我们还提出了该算法的一个改进版本，它能找到一个变分不等式的解，该解也是给定非扩张映射的不动点。我们为这两种算法建立了弱收敛定理。
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