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Entropic approximation for mathematical programs with robust equilibrium constraints

Liu, Y. & Xu, H. (2014). Entropic approximation for mathematical programs with robust equilibrium constraints. SIAM Journal on Optimization, 24(3), pp. 933-958. doi: 10.1137/130931011

Abstract

In this paper, we consider a class of mathematical programs with robust equilibrium constraints represented by a system of semi-infinite complementarity constraints (SIC C). We propose a numerical scheme for tackling SICC. Specific ally, by relaxing the complementarity constraints and then randomizing the index set of SICC, we employ the well-known entropic risk measure to approximate the semi-infinite onstraints with a finite number of stochastic inequality constraints. Under some moderate conditions, we quantify the approximation in term s of the feasible set and the optimal value. The approximation scheme is then applied to a class of two stage stochastic mathematical programs with complementarity constraints in combination with the polynomial decision rules. Finally, we extend the discussion to a mathematical program with distributionally robust equilibrium constraints which is essentially a one stage stochastic program with semi-infinite stochastic constraints indexed by some probability measures from an ambiguity set defined through the KL-divergence.

Publication Type: Article
Additional Information: Copyright Society for Industrial and Applied Mathematics 2014
Publisher Keywords: Entropic risk measure, robust equilibrium constraints, polynomial decision rule, stability analysis, KL-divergence
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering
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