Duality for Composite Optimization Problem within the Framework of Abstract Convexity

2022/09/06 by The Hung Tran, Tran, The Hung, Ewa M. Bednarczuk +1
Computer Science · Mathematics · #Optimization and Variational Analysis #Mathematical Inequalities and Applications #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.2209.02177

Abstract

We study conjugate and Lagrange dualities for composite optimization problems within the framework of abstract convexity. We provide conditions for zero duality gap in conjugate duality. For Lagrange duality, intersection property is applied to obtain zero duality gap. Connection between Lagrange dual and conjugate dual is also established. Examples related to convex and weakly convex functions are given.

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