A stochastic dual dynamic programming method for two-stage distributionally robust optimization problems. (2nd September 2020)

• Record Type: Journal Article
• Authors: Tong, Xiaojiao; Yang, Liu; Luo, Xiao; Rao, Bo
• Is Part Of: Optimization methods and software. Volume 35:Number 5(2020)
• Page Start: 1002
• Page End: 1021
• Publication Date: 2020-09-02
• Subjects: Two-stage distributionally robust optimization (TDRO) -- CVaR-based SAA model -- stochastic dual dynamic programming (SDDP); 90C31 -- 90C05 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1811705
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : This paper studies a class of two-stage distributionally robust optimization (TDRO) problems which comes from many practical application fields. In order to set up some implementable solution method, we first transfer the TDRO problem to its equivalent robust counterpart (RC) by the duality theorem of optimization. The RC reformulation of TDRO is a semi-infinite stochastic programming. Then we construct a conditional value-at-risk-based sample average approximation model for the RC problem. Furthermore, we analyse the error bound of the approximation model and obtain the convergent results with respect to optimal value and optimal solution set. Finally, a so-called stochastic dual dynamic programming approach is proposed to solve the approximate model. Numerical results validate the solution approach of this paper.