Characterisation of zero duality gap for optimization problems in spaces without linear structure
Ewa M. Bednarczuk, Monika Syga · arXiv (Cornell University) · 2024
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 $Φ$-convexity theory and minimax theorems for $Φ$-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.