Existence of optimal solutions and duality results under weak conditions (Q1591355)

The author considers an ordinary convex program with a finite infimum. He defines a class \({\mathcal F}\) of convex functions \(f:\mathbb{R}^N \to\mathbb{R} \cup\{ +\infty\}\) for which the associated program has a solution and has no duality gap. The class \({\mathcal F}\) contains, among others, quadratic convex functions and polynomial convex functions. No regularity condition is assumed.