关于求解伪单调变分不等式的外梯度法的弱收敛性
On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities.
作者信息
Vuong Phan Tu
机构信息
Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria.
出版信息
J Optim Theory Appl. 2018;176(2):399-409. doi: 10.1007/s10957-017-1214-0. Epub 2018 Jan 18.
In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251-263, 2016).
在无限维希尔伯特空间中，我们证明了用于求解伪单调变分不等式的外梯度法所生成的迭代序列弱收敛于一个解。考虑了一类伪单调变分不等式以说明收敛行为。本笔记中得到的结果扩展了文献中一些近期的结果；特别地，它对Khanh（《越南数学学报》41:251 - 263，2016）中提出的一个问题给出了肯定的回答。
Zotero 插件