Duality for constrained robust sum optimization problems

• 成果类型: Article
• 署名作者: Dinh, N.; Goberna, M. A.; Long, D. H.; Volle, M.
• 署名单位: Vietnam National University Ho Chi Minh City (VNUHCM) System; Universitat d'Alacant; Vietnam National University Ho Chi Minh City (VNUHCM) System; Tien Giang University; Avignon Universite
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01494-1
• 发表日期: 2021
• 页码: 271-297
• 关键词: valadier-like formulas; convex; conjugate

摘要

Given an infinite family of extended real-valued functions fi, i. I, and a familyHof nonempty finite subsets of I, the H-partial robust sum of fi, i. I, is the supremum, for J. H, of the finite sums j. J f j. These infinite sums arise in a natural way in location problems as well as in functional approximation problems, and include as particular cases the well-known sup function and the so-called robust sum function, corresponding to the set H of all nonempty finite subsets of I, whose unconstrained minimization was analyzed in previous papers of three of the authors (https:// doi.org/ 10.1007/s11228- 019- 00515-2 and https://doi.org/ 10.1007/s00245- 019- 09596-9). In this paper, we provide ordinary and stable zero duality gap and strong duality theorems for the minimization of a given H-partial robust sum under constraints, as well as closedness and convex criteria for the formulas on the subdifferential of the supfunction.