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Entropic approximation for mathematical programs with robust equilibrium constraints

Liu, Y. and 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


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 Mathematics, Computer Science & Engineering > Engineering
Text - Accepted Version
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