Optimality Conditions and Lagrange Dualities for Optimization Problems Involving Φc-convex Functions

In this paper, we consider an optimization problem in which the objective is the difference of two Φc-convex functions and the constraints include a set constraint and a cone constraint. We first introduce three new constraint qualifications regarding the c-subdifferential and the epigraph propertie...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 207; H. 1; S. 5
Hauptverfasser: Hu, Ling-Li, Fang, Dong-Hui
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer Nature B.V 01.10.2025
Schlagworte:
Constraints
Convex analysis
Mathematical functions
Optimization
Qualifications
ISSN:0022-3239, 1573-2878
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Zusammenfassung:In this paper, we consider an optimization problem in which the objective is the difference of two Φc-convex functions and the constraints include a set constraint and a cone constraint. We first introduce three new constraint qualifications regarding the c-subdifferential and the epigraph properties of the involved functions. Under the new constraint qualifications, we provide some sufficient conditions for optimality conditions to hold. Similarly, strong and total Lagrange dualities for the optimization problem involving the difference of two Φc-convex functions are also given.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02755-9