- Title
- Relaxed lagrangian duality in convex infinite optimization : reducibility and strong duality
- Creator
- Dinh, Nguyen; Goberna, Miguel; López-Cerdá, Marco; Volle, Michel
- Date
- 2023
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/189834
- Identifier
- vital:17482
- Identifier
-
https://doi.org/10.1080/02331934.2022.2031192
- Identifier
- ISSN:0233-1934 (ISSN)
- Abstract
- We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family (Formula presented.) of finite subsets of T, a suitable Lagrangian-Haar dual problem. We obtain necessary and sufficient conditions for (Formula presented.) -reducibility, that is, equivalence to some subproblem obtained by replacing the whole index set T by some element of (Formula presented.). Special attention is addressed to linear optimization, infinite and semi-infinite, and to convex problems with a countable family of constraints. Results on zero (Formula presented.) -duality gap and on (Formula presented.) -(stable) strong duality are provided. Examples are given along the paper to illustrate the meaning of the results. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
- Publisher
- Taylor and Francis Ltd.
- Relation
- Optimization Vol. 72, no. 1 (2023), p. 189-214
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2022 Informa UK Limited
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; 4903 Numerical and computational mathematics; Convex infinite programming; Haar duality; Lagrangian duality; Reducibility
- Full Text
- Reviewed
- Funder
- This research was supported by the Vietnam National University HoChiMinh City (VNU-HCM) [grant number B2021-28-03], 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).
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