伟德线上平台、所2020年系列學術活動（第226場）：孫海琳 教授 南京師範大學
報告題目：Decomposition Methods for Solving Two-Stage Distributionally Robust Optimization Problems
報 告 人：孫海琳 教授 南京師範大學
報告時間：2020 年9 月25 日上午 10：45-11：20
報告地點：騰訊會議 ID：870 938 043
會議密碼：9999
校内聯系人：宋海明 songhaiming@jlu.edu.cn
報告摘要：
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.
報告人簡介：
孫海琳，南京師範大學數學科學學院教授。他于2007年在伟德线上平台獲學士學位，2013年畢業于哈爾濱工業大學數學系，獲博士學位。在其博士期間，他在英國南安普頓大學和香港理工大學聯合培養。2015年12月至2018年1月在香港理工大學應用數學系做博士後研究。2018年獲中國運籌學會青年科技獎和江蘇省數學成就獎。他的研究領域包括随機優化，分布魯棒優化、随機變分不等式及其在投資組合、風險管理和經濟學模型上的應用。他在包括Mathematical Programming、SIAM Journal on Optimization、Mathematics of Operations Research等國際權威期刊發表了多篇論文。他還是多個國際權威學術期刊的審稿人。
