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Journal of Convex Analysis 15 (2008), No. 2, 235--262
Copyright Heldermann Verlag 2008

Farkas-Type Results and Duality for DC Programs with Convex Constraints

Nguyen Dinh
Dept. of Mathematics, National University, Ho Chi Minh City, Vietnam

Guy Vallet
Laboratory of Applied Mathematics, University of Pau, BP 1155, 64013 Pau, France

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

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.

Keywords: Generalized Farkas lemmas, DC-programs, Toland, Fenchel, Lagrange duality, approximate normal cones.

MSC: 49K30, 90C25, 90C26, 90C46

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