- Title
- New glimpses on convex infinite optimization duality
- Creator
- Goberna, Miguel; López, Marco; Volle, Michel
- Date
- 2015
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/97141
- Identifier
- vital:10170
- Identifier
-
https://doi.org/10.1007/s13398-014-0194-2
- Identifier
- ISSN:1578-7303
- Abstract
- Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that (P)=max(D), (P)=max(Q), and (P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing (P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described. © 2014, Springer-Verlag Italia.
- Publisher
- Springer-Verlag Italia
- Relation
- Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas Vol. 109, no. 2 (2015), p. 431-450
- Rights
- Copyright © 2014, Springer-Verlag Italia.
- Rights
- This metadata is freely available under a CCO license
- Subject
- Convex infinite programming; Duality
- Reviewed
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