报告地点：#腾讯会议：960-760-886
邀请人：孙海琳教授
报告摘要：Preference robust optimization (PRO) deals with the case where the decision maker’s utility/risk preference is ambiguous and the optimal decision is based on the worst-case utility function/risk measure from an ambiguity set of plausible utility functions/risk measures constructed with partially available information. In practice, the true utility function/risk measure which captures the DM’s preferences might not exist either because the DM’s preferences are inconsistent or because there are measurement errors in the preference elicitation process. In this work, we propose to randomize the DM’s utility function/risk measure by introducing some random parameters in their definitions and then consider the mean value of the random utility/risk measure. In the absence of complete information of the random parameters, we propose distributionally robust models where the optimal decision is based on the worst-case probability distribution of the random utility function/risk measures. We begin with a distributional preference robust utility model and discuss in detail how an ambiguity set may be constructed with ellipsoidal method and Bootstrap method and how the distributional robust maximin problem may be reformulated as tractable optimization problems. We then move on to discuss randomization of spectral risk measure (SRM) and associated optimization problems. Specifically, we randomize the risk spectrum which characterizes SRM and then consider the mean of the subsequent randomized SRM (RSRM). In the case when the probability distribution is ambiguous, we propose distributionally robust models for the RSRM and computational methods for calculating the DRSRMs and solving related minimax optimization problems. Finally, we present some numerical test results to demonstrate performances of the proposed distributionally robust models and computational schemes. The proposed distributionally robust models not only overcome the preference inconsistency issues but also address potential conservatism of the existing PRO models.
报告人简介：Huifu Xu is a Professor of the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. Prior to joining CUHK in 2019, he was a professor of operational research in the School of Mathematical Sciences, University of Southampton. He received a PhD degree from University of Ballarat (Federation University Australia) in 1999 and worked as a postdoctoral research fellow in the Australian Graduate School of Management (1999-2022). Huifu Xu’s research is mainly on optimal decision making under uncertainty including stochastic mathematical programs with equilibrium constraints (SMPEC), stochastic generalized equations and distributionally robust optimization with applications in energy markets. More recently, he is actively working on preference robust optimization and statistical robustness in data-driven problems. He is an associate editor of Computational Management Science and Mathematical Programming.
