QUANTITATIVE STABILITY ANALYSIS FOR DISTRIBUTIONALLY ROBUST OPTIMIZATION WITH MOMENT CONSTRAINTS

Indexed by:Journal Article

Date of Publication:2016-01-01

Journal:SIAM JOURNAL ON OPTIMIZATION

Included Journals:EI、SCIE

Volume:26

Issue:3

Page Number:1855-1882

ISSN:1052-6234

Key Words:distributionally robust optimization; moment conditions with cone constraints; Holder continuity of the optimal value function; outer semicontinuity of the set of optimal solutions; quantitative stability analysis

Abstract:In this paper we consider a broad class of distributionally robust optimization (DRO) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is defined through parametric moment conditions with generic cone constraints. Under some moderate conditions, including Slater-type conditions of a cone constrained moment system and Holder continuity of the underlying random functions in the objective and moment conditions, we show local Holder continuity of the optimal value function of the inner maximization problem with respect to (w.r.t.) the decision vector and other parameters in moment conditions, and local Holder continuity of the optimal value of the whole minimax DRO w.r.t. the parameter. Moreover, under the second order growth condition of the Lagrange dual of the inner maximization problem, we demonstrate and quantify the outer semicontinuity of the set of optimal solutions of the minimax DRO w.r.t. variation of the parameter. Finally, we apply the established stability results to two particular classes of DRO problems.