Second-order optimality conditions for general nonconvex optimization problems and variational analysis of disjunctive systems
Optimization and Control
2022-11-24 v2
Abstract
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our conditions prove to be sufficient, for an essential local minimizer of second order, under merely basic smoothness and closedness assumptions on the data defining the problem.In the second part, we propose a comprehensive first- and second-order variational analysis of disjunctive systems and demonstrate how the second-order objects appearing in the optimality conditions can be effectively computed in this case.
Cite
@article{arxiv.2203.10015,
title = {Second-order optimality conditions for general nonconvex optimization problems and variational analysis of disjunctive systems},
author = {Matus Benko and Helmut Gfrerer and Jane Ye and Jin Zhang and Jinchuan Zhou},
journal= {arXiv preprint arXiv:2203.10015},
year = {2022}
}