摘要
本文提出了一种镜像梯度下降梯度上升算法来求解单边相对光滑的非凸-凹极小极大问题。在算法的每次迭代中,我们采用镜像梯度下降步来更新相对光滑的变量,采用梯度上升投影步来更新目标函数中光滑的变量。本文在理论上证明了算法收敛到ε-近似一阶稳定点的迭代复杂度是O(ε^(-4))。
In this paper,we propose a mirror descent gradient ascent algorithm to solve one side relatively smooth nonconvex-concave minimax optimization problems.At each iteration of the proposed algorithm,a mirror descent step is performed to update the relatively smooth variable,while a gradient ascent projection step is used to update the smooth variable alternately.We also prove that the iteration complexity of the proposed algorithm is O(ε^(-4))to achieve an e-approximate first-order stationary point.
作者
徐洋
王军霖
徐姿
XU Yang;WANG Junlin;XU Zi(Department of Mathematics,College of Sciences,Shanghai University,Shanghai 200444,China)
出处
《运筹学学报（中英文）》
CSCD
北大核心
2024年第1期18-28,共11页
Operations Research Transactions
基金
国家自然科学基金(No.12071279)
上海市自然科学基金(No.20ZR1420600)。
关键词
非凸-凹极小极大问题
相对光滑
镜像梯度法
nonconvex-concave minimax optimization problem
relatively smooth
mirror gradient method
