Stable and Total Fenchel Duality for DC Optimization Problems in Locally Convex Spaces
D. H. Fang, C. Li, Xiaoqi Yang · SIAM Journal on Optimization · 2011
We consider the DC (difference of two convex functions) optimization problem [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are proper convex functions defined on locally convex Hausdorff topological vector spaces [Formula: see text] and [Formula: see text], and [Formula: see text] is a linear continuous operator from [Formula: see text] to [Formula: see text]. Adopting different tactics, two types of the Fenchel dual problems of [Formula: see text] are given. By using the properties of the epigraph of the conjugate functions, some sufficient and necessary conditions for the weak duality of [Formula: see text] are provided. Sufficient and/or necessary conditions for the strong Fenchel duality, the stable Fenchel duality, and the stable total duality are derived.