Stable and Total Fenchel Duality for Convex Optimization Problems in Locally Convex Spaces
Chong Li, Donghui Fang, Genaro López-Acedo, Marco A. López · SIAM Journal on Optimization · 2009
We consider the optimization problem $(P_{A})$ $\inf_{x\in X}\{f(x)+g(Ax)\}$ where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y, respectively, and A is a linear operator from X to Y. By using the properties of the epigraph of the conjugated functions, some sufficient and necessary conditions for the strong Fenchel duality and the strong converse Fenchel duality of $(P_{A})$ are provided. Sufficient and necessary conditions for the stable Fenchel duality and for the total Fenchel duality are also derived.