In this paper, we introduce the second-order subdifferentials for functions which are G\^ateaux differentiable on an open set and whose G\^ateaux derivative mapping is locally Lipschitz. Based on properties of this kind of second-order subdifferentials and techniques of variational analysis, we derive second-order necessary conditions for weak Pareto efficient solutions of multiobjective programming problems with constraints.
@article{arxiv.1909.09795,
title = {Second-order optimality conditions for multiobjective optimization problems with constraints},
author = {Nguyen Quang Huy and Bui Trong Kien and Gue Myung Lee and Nguyen Van Tuyen},
journal= {arXiv preprint arXiv:1909.09795},
year = {2019}
}