Abstract

We are interested in new versions of Farkas lemmas for systems involving convex and DC-inequalities. These versions extend well-known Farkas-type results published recently, which were used as main tools in the study of convex optimization problems. The results are used to derive several strong duality results such as: Lagrange, Fenchel-Lagrange or Toland-Fenchel-Lagrange duality for DC and convex problems. Moreover, it is shown that for this class of problems, these versions of Farkas lemma are actually equivalent to several strong duality results of Lagrange, Fenchel-Lagrange or Toland-Fenchel-Lagrange types.

Author information

Contact details are reproduced from the original publication and may be historical.

Nguyen Dinh

Department of Mathematics, International University, Vietnam National University, Ho Chi Minh City, Vietnam

ndinh@hcmiu.edu.vn

Guy Vallet

Laboratory of Applied Mathematics, University of Pau, BP 1155, 64013 Pau, France
and: UMR-CNRS 5142, Pau, France

guy.vallet@univ-pau.fr

T. T. A. Nghia

Dept. of Mathematics and Computer Science, University of Pedagogy, Ho Chi Minh City, Vietnam

ttannghia@gmail.com

Keywords

  • Generalized Farkas lemmas
  • DC-programs
  • Toland
  • Fenchel
  • Lagrange duality
  • approximate normal cones

Mathematics Subject Classification

49K30, 90C25, 90C26, 90C46

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Suggested citation

N. Dinh, G. Vallet, T. T. A. Nghia. “Farkas-Type Results and Duality for DC Programs with Convex Constraints.” Journal of Convex Analysis 15 (2008), No. 2, 235–262. https://doi.org/10.68381/jca15017

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