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

Ewa Bednarczuk () and Monika Syga ()
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Ewa Bednarczuk: Polish Academy of Sciences
Monika Syga: Warsaw University of Technology

Journal of Global Optimization, 2025, vol. 92, issue 1, No 6, 135-158

Abstract: Abstract 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 $$\Phi $$ Φ -convexity theory and we formulate our zero duality gap conditions in terms of elementary functions $$\varphi \in \Phi $$ 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.

Keywords: Abstract convexity; Minimax theorem; Lagrangian duality; Augmented Lagrangians; Zero duality gap; Weak duality; Prox-regular functions; Paraconvex and weakly convex functions; Kantorovich duality; Wasserstein distance (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01477-6

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