Strong and total duality for constrained composed optimization via a coupling conjugation scheme

Based on a coupling conjugation scheme and the perturbational approach, we build Fenchel-Lagrange dual problem of a composed optimization model with infinite constraints in separated locally convex spaces. This paper has mainly two targets. One is to establish strong duality under a new regularity c...

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Bibliographic Details
Published inOptimization Vol. 73; no. 2; pp. 267 - 294
Main Authors You, Manxue, Li, Genghua
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.02.2024
Taylor & Francis LLC
Subjects
Conjugation
Constrained composed optimization
Constraints
Coupling
evenly convex function
generalized convex conjugation
Operators (mathematics)
Optimization models
regularity condition
strong and total duality
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Summary:Based on a coupling conjugation scheme and the perturbational approach, we build Fenchel-Lagrange dual problem of a composed optimization model with infinite constraints in separated locally convex spaces. This paper has mainly two targets. One is to establish strong duality under a new regularity condition ( $ {\rm RC}_A $ RC A ) and an extension closed-type condition ( $ {\rm ECRC}_A $ ECRC A ). The e-convex counterpart of Fenchel-Moreau theorem plays a key role in analysing the relation between them. The other aim is to achieve the sufficient and necessary characterizations for total duality in terms of c-subdifferentials. For this purpose, a formula for ε-c-subdifferentials of a proper function composed with a linear continuous operator is proved and applied.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2103416