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In this talk, a review of an approximation scheme for solving maxinf (minsup) optimization problems is presented. The family of the problems that can be modeled under this setting is appealingly large, ranging from linear and nonlinear complementarity problems, fixed points, variational inequalities, equilibrium problems, as well as optimization under stochastic ambiguity, robust optimization, risk-based optimization, and semi-infinite optimization.

The mathematical programming problem is set to find a maxinf (minsup) point of a bifunction. Given this setting, a solution strategy is proposed using an approximation scheme, based on the application of lopsided convergence theory. The first definition of lopsided convergence was established during the eighties [1] for extended real value bifunctions, then revised by 2010 [5, 6], for finite value functions over product sets. Lately, it was revisited [9, 8, 7], by extending the definition to more general domains and proposing an associated metric, the lopsided distance. Finally, some numerical results are presented for three examples: 1) a general equilibrium model for an exchange economy with uncertainty [2]; 2) a general equilibrium model with financial markets [3]; and 3) an infrastructure planning for fast EV-charging station problems [4].

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