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Sequential Farkas lemmas for convex systems

Dinh Nguyen 1, *
Mo Hong Tran 2
  1. International University, VNU-HCM
  2. Tien Giang University, Tien Giang province
Correspondence to: Dinh Nguyen, International University, VNU-HCM. Email: pvphuc@vnuhcm.edu.vn.
Volume & Issue: Vol. 17 No. 4 (2014) | Page No.: 20-26 | DOI: 10.32508/stdj.v17i4.1552
Published: 2014-12-31

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Copyright The Author(s) 2023. This article is published with open access by Vietnam National University, Ho Chi Minh city, Vietnam. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0) which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. 

Abstract

In this paper we introduce two new versions of Farkas lemma for two kinds of convex systems in locally convex Hausdorff topological vector spaces which hold without any constraint qualification conditions. These versions hold in the limits and will be called sequential Farkas lemmas. Concretely, we establish sequential Farkas lemmas for cone-convex systems and for systems which are convex with respect to a sublinear function. The first result extends some known ones in the literature while the second is a new one.

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