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arXiv · 2307.15389

On new generalized differentials with respect to a set and their applications

Xiaolong Qin·Vo Duc Thinh·Jen-Chih Yao
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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.

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Xiaolong Qin, Vo Duc Thinh, Jen-Chih Yao. 2023-07-28. On new generalized differentials with respect to a set and their applications. https://arxiv.org/abs/2307.15389

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