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arXiv · 2311.08741

Formulas for calculating of generalized differentials with respect to a set and their applications

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

This paper provides formulas for calculating of Fr\'{e}chet and limiting normal cones with respect to a set of sets and the limiting coderivative with respect to a set of set-valued mappings. These calculations are obtained under some qualification constraints and are expressed in the similar forms of these ones of Fr\'{e}chet and limiting normal cones and the limiting coderivative. By using these obtained formulas, we state explicit necessary optimality conditions with respect to a set for optimization problems with equilibrium constraints under certain qualification conditions. Some illustrated examples to obtained results are also established.

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Vo Duc Thinh, Xiaolong Qin, Jen-Chih Yao. 2023-11-15. Formulas for calculating of generalized differentials with respect to a set and their applications. https://arxiv.org/abs/2311.08741

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