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Under some moderate conditions, we quantify the approximation in terms 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.<\/jats:p>","DOI":"10.1137\/130931011","type":"journal-article","created":{"date-parts":[[2014,7,3]],"date-time":"2014-07-03T14:05:58Z","timestamp":1404396358000},"page":"933-958","source":"Crossref","is-referenced-by-count":13,"title":["Entropic Approximation for Mathematical Programs with Robust Equilibrium Constraints"],"prefix":"10.1137","volume":"24","author":[{"given":"Yongchao","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huifu","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,7,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-004-0488-7"},{"key":"atypb2","unstructured":"E. 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