- Title
- New Farkas-type results for vector-valued functions : A non-abstract approach
- Creator
- Dinh, Nguyen; Goberna, Miguel; Long, Dang; Lopez-Cerda, Marco
- Date
- 2019
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/170548
- Identifier
- vital:14145
- Identifier
-
https://doi.org/10.1007/s10957-018-1352-z
- Identifier
- ISBN:0022-3239
- Abstract
- This paper provides new Farkas-type results characterizing the inclusion of a given set, called contained set, into a second given set, called container set, both of them are subsets of some locally convex space, called decision space. The contained and the container sets are described here by means of vector functions from the decision space to other two locally convex spaces which are equipped with the partial ordering associated with given convex cones. These new Farkas lemmas are obtained via the complete characterization of the conic epigraphs of certain conjugate mappings which constitute the core of our approach. In contrast with a previous paper of three of the authors (Dinh et al. in J Optim Theory Appl 173:357-390, 2017), the aimed characterizations of the containment are expressed here in terms of the data.
- Publisher
- Springer
- Relation
- Journal of Optimization Theory and Applications Vol. 182, no. 1 (2019), p. 4-29
- Rights
- Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2018
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0906 Electrical and Electronic Engineering; Farkas-type results; Vector-valued functions; Qualification conditions
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