Duality for extended infinite monotropic optimization problems

• 成果类型: Article
• 署名作者: Dinh The Luc; Volle, Michel
• 署名单位: Ton Duc Thang University; Ton Duc Thang University; Avignon Universite
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01557-3
• 发表日期: 2021
• 页码: 409-432
• 关键词: flow problems

摘要

We establish necessary and sufficient conditions for strong duality of extended monotropic optimization problems with possibly infinite sum of separable functions. The results are applied to a minimization problem of the infinite sum of proper convex functions. We consider a truncation method for duality and obtain the zero duality gap by using only dual variable of finite support. An application to minimum cost flow problems in infinite networks is also discussed.