Liu, Y. & Xu, H. (2014). Entropic approximation for mathematical programs with robust equilibrium constraints. SIAM Journal on Optimization, 24(3), pp. 933958. doi: 10.1137/130931011

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Abstract
In this paper, we consider a class of mathematical programs with robust equilibrium constraints represented by a system of semiinfinite 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 wellknown entropic risk measure to approximate the semiinfinite 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 semiinfinite stochastic constraints indexed by some probability measures from an ambiguity set defined through the KLdivergence.
Item Type:  Article 

Additional Information:  Copyright Society for Industrial and Applied Mathematics 2014 
Uncontrolled Keywords:  Entropic risk measure, robust equilibrium constraints, polynomial decision rule, stability analysis, KLdivergence 
Subjects:  T Technology > TA Engineering (General). Civil engineering (General) 
Divisions:  School of Engineering & Mathematical Sciences > Engineering 
URI:  http://openaccess.city.ac.uk/id/eprint/3267 
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