Optimality conditions based on the Fr\'echet second-order subdifferential
Abstract
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is -smooth, we show that strengthened second-order necessary optimality conditions are valid if the constraint set is generalized polyhedral convex. For problems in a new setting, where the objective function is just assumed to be -smooth and the constraint set is generalized polyhedral convex, we establish sharp second-order necessary optimality conditions based on the Fr\'echet second-order subdifferential of the objective function and the second-order tangent set to the constraint set. Three examples are given to show that the used hypotheses are essential for the new theorems. Our second-order necessary optimality conditions refine and extend several existing results.
Cite
@article{arxiv.2007.14593,
title = {Optimality conditions based on the Fr\'echet second-order subdifferential},
author = {Duong Thi Viet An and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:2007.14593},
year = {2020}
}