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Convergence Analysis For Mathematical Programs With Distributionally Robust Chance Constraint


Academic report of Haitian scholars


Report title: Convergence Analysis For Mathematical Programs With Distributionally Robust Chance Constraint


Report: XU Huifu (School of Mathematical Sciences, University of Southampton, UK)


Report time: July 29, 2016 AM 10:00-11:00


Location: A1101#room, Innovation Park Building


Contact: Prof. ZHANG Liwei (tel: 84708351-8118)


Abstract: Convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literrature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance constraints where the true probability is unkown, but it is possible to construct an ambiguity set of distributions and the chance is based on the most conservative selection of probability distribution from ambiguity set. The convergence analysis focuses on impact of the variation of the ambiguity set on the optimal value and the optimal solutions. We start by deriving general convergence results under abstract conditions such as continuity of the robust probability functions and uniform convergence of robust probability functions and followed with detailed analysis of these conditions. Two sufficient conditions have been derived with one applicable to both continuous and discrete probability distribution and the other to continuous distribution but different from the well known traditional boundary condition in the literature. Case studies are carried out for ambiguity sets being constructed through moments and samples.


Brief introduction to the reporter: Dr. XU Huifu is a professor of college of mathematics sciences in Southampton University and Haitian Scholar of school of mathematics sciences in Dalian University of Technology. Prof. XU is an international famous optimization expert, and he has devoted himself to optimization research for 26 years, proceeded comprehensive research on mathematical programming problem with equilibrium constraint, optimization problem with stochastic dominant constraint and Robust optimization problem. He has acquired many innovated achievements. Prof. XU has already published more than 70 papers on international top magazines such as Mathematical Programming Mathematics of Operations Research, SIAM J. Optimization, JOTA etc. He has been invited to make speeches in international high-level academic conferences many times. He works as an editional board member for international academic journals such as Computational Managements Science by now.