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Frechet Second-Order Subdifferentials of Lagrangian Functions and Optimality Conditions
We establish some new results on second-order (necessary and sufficient) optimality conditions for minimization problems with abstract constraints in infinite-dimensional spaces, where the objective functions are only assumed to be
-smooth. For doing so, we apply the concept of Fréchet (regular) second-order subdifferential from variational analysis to the Lagrangian function of the problem under investigation. Our results extend and refine several existing ones.
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