New Farkas-Type Results for Vector-Valued Functions: A Non-abstract Approach

Nguyen Dinh (), Miguel A. Goberna (), Dang H. Long () and Marco A. López-Cerdá ()
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Nguyen Dinh: International University, Vietnam National University-HCM
Miguel A. Goberna: University of Alicante
Dang H. Long: VNUHCM-University of Science
Marco A. López-Cerdá: University of Alicante

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 1, No 2, 4-29

Abstract: 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.

Keywords: Farkas-type results; Vector-valued functions; Qualification conditions; 90C48; 90C46; 90C29 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-018-1352-z

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