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

• Published in: Journal of global optimization Vol. 92; no. 1; pp. 135 - 158
• Main Authors: Bednarczuk, Ewa, Syga, Monika
• Format: Journal Article
• Language: English
• 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

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...