Fréchet Second-Order Subdifferentials of Lagrangian Functions and Optimality Conditions

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Abstract
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 [Formula: see text]-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.
Funding Information
  • Australian Research Council (DP200100124)
  • National Natural Science Foundation of China (U1811461)
  • National Foundation for Science and Technology Development (101.01-2018.308)
  • Vietnam Academy of Science and Technology (NVCC01.07/22-23)

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