Fréchet Second-Order Subdifferentials of Lagrangian Functions and Optimality Conditions
Duong Thi Viet An, Hong‐Kun Xu, Nguyen Dong Yen · SIAM Journal on Optimization · 2023
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.