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Title: Stable and total Fenchel duality for DC optimization problems in locally convex spaces
Authors: Fang, DH
Li, C
Yang, XQ 
Keywords: Strong Fenchel duality
Total Fenchel duality
Difference of two convex functions programming
Issue Date: 2011
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on optimization, 2011, v. 21, no. 3, p. 730-760 How to cite?
Journal: SIAM journal on optimization 
Abstract: We consider the DC (difference of two convex functions) optimization problem (P)) inf [sub χ∈]X {(ƒ₁ (χ) - ƒ₂(χ)) + (g₁(Aχ) - g₂(Aχ))}, where ƒ₁, ƒ₂, g₁, and g₂ are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y, and A is a linear continuous operator from X to Y. Adopting different tactics, two types of the Fenchel dual problems of (P) are given. By using the properties of the epigraph of the conjugate functions, some sufficient and necessary conditions for the weak duality of (P) are provided. Sufficient and/or necessary conditions for the strong Fenchel duality, the stable Fenchel duality, and the stable total duality are derived.
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/100789749
Rights: © 2011 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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