题 目：Improved variance reduction extragradient method with line search for stochastic variational inequalities

主讲人：蔡邢菊教授，博导

时 间：2023年9月20日（周三），下午14：30-16：30

地 点：旧版草莓无限现看网站203会议室

主讲人简介：蔡邢菊，南京师范大学数学科学学院教授、博导，南京大学计算数学博士，新加坡南洋理工大学访问学者。主要从事最优化理论与算法、变分不等式、数值优化方向的研究工作。先后主持国家青年基金1项、面上基金1项、省青年基金1项，参加国家重点项目1项，获江苏省科技进步奖一等奖1项。兼任江苏省运筹学会理事长，中国运筹学会副秘书长，SCI期刊《Asia-Pacific Journal of Operational Research》客座编委。

报告摘要：The fact that the performance of extragradient method is closely related to the step size motivates us to propose this improved stochastic extragradient method with different step sizes in prediction and correction step. We adopt the line search technique in the prediction step, and for the initial line search step size of each iteration, an adaptive method is adopted. The step size is reduced by the proportion related to the problem to satisfy the line search criterion. Under the assumptions of Lipschitz continuous and pseudo-monotone operator and independent identically distributed sampling, the iterative complexity of O(ε(-1) ) and the oracle complexity of O(ε(-2)) are obtained. For estimating the upper bound of the second order moment of martingale difference sequences, we present a more convenient and comprehensible scheme instead of using Burkholder-Davis-Gundy (BDG) inequality. Moreover, in numerical experiment, the proposed algorithm is used to solve fractional programming problems such as energy efficiency in multiantenna communications. Numerical results show that our algorithm has good numerical performance.