主题：【鲁棒与随机优化系列讲座（三）】Robust Approximation to Chance-Constrained Binary Programming using Non-parametric Density Information

主讲人：西南财经大学 徐亮教授

主持人：华南理工大学 钟远光教授

时间：2021年4月22日（周四）14:00-15:30

直播平台及会议ID：腾讯会议 会议ID：689908 553

主办单位：大数据研究院 科研处

主讲人简介：

Dr. Liang Xu is currently a professor at the Big Data Research Institute of School of Business Administration, The Southwestern University of Finance and Economics (SWUFE). He received a bachelor degree in Mathematics from Beijing Normal University and a master degree in management science in Sun yat-sen University. He received a PhD in Logistics and Maritime Studies from the Hong Kong Polytechnic University. He serves as the director of MBA Center in SWUFE and the assistant director of Big Data Research Institute in SWUFE.

He is interested in the research areas of robust optimization, stochastic models in finance, intelligent investment and intelligent transportation. His papers have been published in journals such as MSOM, TRB, EJOR, NRL,ORL IJPR,JORS, Omega and so on.

His team is now working on development of intelligent investment strategies and system based on big data and optimization technique. He is currently a consultor for Huaxi securities on the risk control in intelligent investment and FoF management. His team has won the second prize for innovation awarded by Banking and Insurance Regulatory Commission.

徐亮，西南财经大学工商管理学院/大数据研究院教授，主要研究领域包括：鲁棒优化、金融随机模型、智能投资和智慧交通等。他的成果发表在MSOM, TRB, EJOR, NRL,ORL IJPR,JORS, Omega等期刊。

内容提要：

A chance-constrained binary program (CCBP) is a general optimization problem over binary decision variables restricted by a chance constraint, which ensures that a linear inequality with uncertain coefficients can be violated only up to a given probability threshold. Despite of its wide applications, the CCBP is very challenging to solve, as a result of its combinatorial nature and the involvement of its chance constraint. For the CCBP, its existing solution methods with tractability guarantees are mainly extended from the methods proposed for problems with continuous decision variables and exploit the parametric information, such as mean and variance, of the uncertain coefficients. In this paper, we propose a general robust optimization framework for the development of solution methods with tractability guarantees for the CCBP. We follow this framework to develop new solution methods for the CCBP. Unlike the existing solution methods, we novely exploit the binary characteristic of the decision variables, as well as non-parametric information about the density function of the uncertain coefficients, so as to devise tight upper bounds on the violation probability of the chance constraint. Based on these upper bounds, we then derive two new robust optimization models to approximate the CCBP, so that both the models can be decomposed into binary programs, and one of them can be decomposed into nominal problems, for which tractability is guaranteed. Computational results show that our newly proposed solution methods produce significantly better solutions to the CCBP than those existing methods.

本次讲座涉及的鲁棒优化问题：使用密度函数的非参信息求解带机会约束的0-1规划。