Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications

This paper provides formulas for calculating Fréchet 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 the...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 203; no. 3; pp. 2784 - 2817
Main Authors: Thinh, Vo Duc, Qin, Xiaolong, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2024
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Cones
Constraining
Constraints
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
90C31
90C30
49J53
Coderivative with respect to a set
Calculation rule
Optimality condition
Normal cone with respect to a set
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper provides formulas for calculating Fréchet 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 the ones of Fréchet and limiting normal cones and the limiting coderivative. By using these new formulas, we state explicit necessary optimality conditions with respect to a set for optimization problems with equilibrium constraints under certain qualification conditions. Some examples are also presented.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02546-8