Topic: Robust Optimization: The Moment Problem and its Recent Advances

Speaker: Prof. Simai He

Location: Room 306, Glorious Sun Building, Yan'an Road Campus

Time: 2020-11-24 09:30:00

Brief introduction of the speaker: Prof. Simai He is currently working in the School of Information Management and Engineering and the School of Interdisciplinary Studies at Shanghai University of Finance and Economics. He received his undergraduate degree from the University of Science and Technology of China and his PhD from the Chinese University of Hong Kong. His main research areas are operations research optimization and supply chain management. He was awarded the Gold Medal of the 33rd International Mathematical Olympiad, the Young Scientist Award of the Operations Research Society of China and the Second Prize of the Ministry of Education for Outstanding Achievements in Humanities and Social Sciences.

Report Overview: Data in management practice, although extremely voluminous, is often of unsatisfactory quality. At the same time, the core parameters assumed in traditional management decision models (e.g. inventory cost of a single product) are often difficult to estimate accurately in practice. Therefore, management decision making in practice based on statistical distribution assumptions or learning algorithms of simple logic inevitably involves certain uncontrollable decision risks. Robust optimization methods can better handle the uncertainty of parameters and distributions.

We first introduce the decision logic and application scenarios of robust optimization methods, and focus on an important research direction of robust optimization: the moment problem. The moment problem is based on the moment information of the distribution, i.e., mean/variance/third-order and higher-order expectation values, to construct the uncertainty set of the distribution and make the corresponding decision based on it. Based on this, we study how to introduce common distributional assumptions in economics and management (single-peaked, log-concave, monotonic loss rate, etc.) and construct numerical methods based on the theoretical structure of optimal solutions. In addition, we investigate how to improve classical probability inequalities using the moment problem and explore the possibility of further improving the central limit convergence speed inequality commonly used in statistics.