On new generalized differentials with respect to a set and their applications
Optimization and Control
2023-07-31 v1 Numerical Analysis
Numerical Analysis
Abstract
The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, based on these normal cones. The necessary and sufficient conditions for the Aubin property with respect to a set of multifunctions are then described by using the limiting coderivative with respect to a set. As a result of the limiting subdifferential with respect to a set, we offer the requisite optimality criteria for local solutions to optimization problems. In addition, we also provide examples to demonstrate the outcomes.
Keywords
Cite
@article{arxiv.2307.15389,
title = {On new generalized differentials with respect to a set and their applications},
author = {Xiaolong Qin and Vo Duc Thinh and Jen-Chih Yao},
journal= {arXiv preprint arXiv:2307.15389},
year = {2023}
}