一、报告题目：Variance-Based Single-Call Proximal ExtragradientAlgorithms for Stochastic Mixed Variational Inequalities

二、报告人：嘉应学院杨振平副教授

三、报告时间：2022年1月14日星期五上午10:00

四、报告平台：腾讯会议会议ID：303-507-559

五、摘要：In the study of stochastic variational inequalities, the extragradient algorithms attractmuch attention. However, such schemes require two evaluations of the expected mappingat each iteration in general. In this paper, we present several variance-basedsingle-call proximal extragradient algorithms for solving a class of stochastic mixedvariational inequalities by aiming at alleviating the cost of an extragradient step. Onesalient feature of the proposed algorithms is that they require only one evaluationof the expected mapping at each iteration, and hence, the computation load may besignificantly reduced. We show that the proposed algorithms can achieve sublinearergodic convergence rate in terms of the restricted merit function. Furthermore, underthe strongly Minty variational inequality condition, we derive some results related toconvergence rate of the distance between iterates and solutions, the iteration and oraclecomplexities for the proposed algorithms when the sample size increases at a geometricor polynomial rate. Numerical experiments indicate that the proposed algorithmsare quite competitive with some existing algorithms.

六、报告人简介：

杨振平，博士，副教授，2019年博士毕业于上海大学。研究兴趣主要是随机变分不等式问题及随机优化问题的数值算法方面的研究，在Journal of Scientific Computing、Journal of Optimization Theory and Applications、Journal of Computational and AppliedMathematics及中国管理科学等国内外权威期刊上发表学术论文10余篇。目前主持国家自然科学基金青年项目1项、广东省自然科学基金面上项目1项和广东省教育厅青年创新人才项目1项。