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

2024/01/09 by Bednarczuk, Ewa, Syga, Monika
#32F17 #49J52 #49K27 #49K35 #52A01 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2401.04806

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 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.

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