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Zbl 1145.49016
Dinh, Nguyen; Vallet, Guy; Nghia, T.T.A.
Farkas-type results and duality for DC programs with convex constraints. (English)
[J] J. Convex Anal. 15, No. 2, 235-262 (2008). ISSN 0944-6532

Summary: 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 type.

MSC 2000:: *49K30 Optimal solutions belonging to restricted classes
90C25 Convex programming
90C26 Nonconvex programming
90C46 Optimality conditions, duality
49N15 Duality theory (optimization)

Keywords: generalized Farkas lemmas; DC-programs; Toland; Fenchel; Lagrange duality; approximate normal cones

Cited in: Zbl 1228.90078

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