报告地点: 腾讯会议 605 844 523
报告摘要：Sample average approximation (SAA) approach for two-stage stochastic variational inequalities (SVIs) with continuous probability distributions, where the second-stage problems have multiple solutions, may not promise convergence assertions as the sample size tends to infinity. In this paper, a regularized SAA approach is proposed to
numerically solve a class of two-stage SVIs with continuous probability distributions, where the second-stage problems are monotone and allowed to havemultiple solutions. We first give some structural properties. After that, the convergence analysis of the regularized SAA approach for two-stage SVIs is investigated as the regularization
parameter tends to zero and the sample size tends to infinity. Finally, we employ the progressive hedging algorithm to report some numerical results.
个人简介：蒋杰, 重庆大学 数学与统计*女王调教-女王调教视频-女王 调教小说 信息与计算科学系, 弘深青年教师。目前正在香港理工大学 中国科*女王调教-女王调教视频-女王 调教小说数学与系统科学研究院-香港理工大学应用数学联合实验室进行博士后访问，合作教授陈小君讲座教授。
研究方向：我主要研究不确定环境下的决策问题，比如，随机规划，随机变分不等式，分布式鲁棒优化，风险厌恶问题等。聚焦于这些问题的，统计特性，定量分析，离散化逼近，算法设计，在实际问题中的应用。最新的研究兴趣是机器学习和深度学习中一些跟随机优化、统计优化相关的领域，比如深度学习中的GANs模型，强化学习，随机算法等。
代表文章：
[1] Jiang J, Chen Z. Quantitative stability analysis of two-stage stochastic linear programs with full random recourse. Numerical Functional Analysis and Optimization, 2019, 40(16): 1847-1876.
[2] Jiang J, Shi Y, Wang X, Chen X, Regularized two-stage stochastic variational inequalities for Cournot-Nash equilibrium under uncertainty. Journal of Computational Mathematics, 2019, 37(6): 813-842.
[3] Jiang J, Chen X, Chen Z. Quantitative analysis for a class of two-stage stochastic linear variational inequality problems. Computational Optimization and Applications, 2020, 76(2): 431–460.
[4] Jiang J, Li S. On complexity of multistage stochastic programs under heavy tailed distributions. Operations Research Letters, 2021, 49(2): 265-269.
[5] Jiang J, Sun H, Zhou B. Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage. To appear in Numerical Algorithms, 2021, doi: 10.1007/s11075-021-01110-z.