Characterisation of zero duality gap for optimization problems in spaces without linear structure

We prove sufficient and necessary conditions ensuring zero Lagrangian duality gap for Lagrangians defined with help of general perturbation functions. This kind of Lagrangians include generalized and augmented Lagrangians. To this aim, we use the Φ -convexity theory and we formulate our zero duality...

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Bibliographic Details
Published inJournal of global optimization Vol. 92; no. 1; pp. 135 - 158
Main Authors Bednarczuk, Ewa, Syga, Monika
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2025
Springer Nature B.V
Subjects
Computer Science
Convex analysis
Convexity
Lagrangian function
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Abstract convexity
Lagrangian duality
Prox-regular functions
Minimax theorem
Weak duality
Augmented Lagrangians
Wasserstein distance
Paraconvex and weakly convex functions
Kantorovich duality
Zero duality gap
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Summary:We prove sufficient and necessary conditions ensuring zero Lagrangian duality gap for Lagrangians defined with help of general perturbation functions. This kind of Lagrangians include generalized and augmented Lagrangians. To this aim, we use the Φ -convexity theory and we formulate our zero duality gap conditions in terms of elementary functions φ ∈ Φ . The obtained results apply to optimization problems involving prox-bounded functions, DC functions, weakly convex functions and paraconvex functions as well as infinite-dimensional linear optimization problems, including Kantorovich duality which plays an important role in determining Wasserstein distance.
Bibliography:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-025-01477-6