Abstract
This paper deals with generalized semi-infinite optimization problems where the (infinite) index set of inequality constraints depends on the state variables and all involved functions are twice continuously differentiable. Necessary and sufficient second-order optimality conditions for such problems are derived under assumptions which imply that the corresponding optimal value function is second-order (parabolically) directionally differentiable and second-order epiregular at the considered point. These sufficient conditions are, in particular, equivalent to the second-order growth condition.
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Rückmann, JJ., Shapiro, A. Second-Order Optimality Conditions in Generalized Semi-Infinite Programming. Set-Valued Analysis 9, 169–186 (2001). https://doi.org/10.1023/A:1011239607220
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DOI: https://doi.org/10.1023/A:1011239607220