Duality for constrained robust sum optimization problems
| Autor: | Michel Volle, Nguyen Nang Dinh, Dang H. Long, Miguel A. Goberna |
|---|---|
| Přispěvatelé: | Universidad de Alicante. Departamento de Matemáticas, Laboratorio de Optimización (LOPT), Vietnam National University - Ho Chi Minh City (VNU-HCM), Fundació per a la Investigació i la Docència Maria Angustias Giménez [Barcelone] (FIDMAG), FIDMAG Germanes Hospitalaries, Laboratoire Polymères et Matériaux Avancés (LPMA), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), EA2151 Laboratoire de Mathématiques d'Avignon (LMA), Avignon Université (AU) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Optimization problem
General Mathematics 0211 other engineering and technologies Duality (optimization) Stable strong duality theorems 010103 numerical & computational mathematics 02 engineering and technology Subderivative 01 natural sciences Combinatorics Robust sum optimization problems Sup-functions Estadística e Investigación Operativa Strong duality 0101 mathematics Stable zero duality gap ComputingMilieux_MISCELLANEOUS Mathematics 021103 operations research Duality gap Numerical analysis Regular polygon Infimum and supremum [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Partial robust sums of families of functions Software |
| Zdroj: | RUA. Repositorio Institucional de la Universidad de Alicante Universidad de Alicante (UA) Mathematical Programming Mathematical Programming, Springer Verlag, 2021, 189 (1-2), pp.271-297. ⟨10.1007/s10107-020-01494-1⟩ |
| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-020-01494-1⟩ |
| Popis: | Given an infinite family of extended real-valued functions fi, i∈I, and a family H of 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∈Jfj. 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 sup-function. This research was supported by the National Foundation for Science & Technology Development (NAFOSTED), Vietnam, Project 101.01-2018.310, and by Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI), and European Regional Development Fund (ERDF), Project PGC2018-097960-B-C22. |
| Databáze: | OpenAIRE |
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