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arXiv · 2401.04806

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

Ewa Bednarczuk·Monika Syga
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Abstract

We prove sufficient and necessary conditions ensuring zero duality gap for Lagrangian duality in some classes of nonconvex optimization problems. To this aim, we use the $\Phi$-convexity theory and minimax theorems for $\Phi$-convex functions. The obtained zero duality 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.

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Ewa Bednarczuk, Monika Syga. 2024-01-09. Characterisation of zero duality gap for optimization problems in spaces without linear structure. https://arxiv.org/abs/2401.04806

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