必威、所2020年系列学术活动（第226场）：孙海琳 教授 南京师范大学
报告题目：Decomposition Methods for Solving Two-Stage Distributionally Robust Optimization Problems
报 告 人：孙海琳 教授 南京师范大学
报告时间：2020 年9 月25 日上午 10：45-11：20
报告地点：腾讯会议 ID：870 938 043
会议密码：9999
校内联系人：宋海明 songhaiming@jlu.edu.cn
报告摘要：
Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems. In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. This is achieved by introducing nonanticipativity constraint for the first stage decision variables, rearranging the minimax problem through Lagrange decomposition and applying the well-known primal-dual hybrid gradient (PDHG) method to the new minimax problem. The algorithmic framework does not depend on specific structure of the ambiguity set. To extend the algorithm to the case that the underlying random variables are continuously distributed, we propose a discretization scheme and quantify the error arising from the discretization in terms of the optimal value and the optimal solutions when the ambiguity set is constructed through generalized prior moment conditions, the Kantorovich ball and $\phi$-divergence centred at an empirical probability distribution. Some preliminary numerical tests show the proposed decomposition algorithm featured with parallel computing performs well.
报告人简介：
孙海琳，南京师范大学数学科学学院教授。他于2007年在必威官网获学士学位，2013年毕业于哈尔滨工业大学数学系，获博士学位。在其博士期间，他在英国南安普顿大学和香港理工大学联合培养。2015年12月至2018年1月在香港理工大学应用数学系做博士后研究。2018年获中国运筹学会青年科技奖和江苏省数学成就奖。他的研究领域包括随机优化，分布鲁棒优化、随机变分不等式及其在投资组合、风险管理和经济学模型上的应用。他在包括Mathematical Programming、SIAM Journal on Optimization、Mathematics of Operations Research等国际权威期刊发表了多篇论文。他还是多个国际权威学术期刊的审稿人。
