Strong Duality in Cone Constrained Nonconvex Optimization
Fabián Flores-Bazán, Giandomenico Mastroeni · SIAM Journal on Optimization · 2013
In this paper we deepen the analysis of the conditions that ensure strong duality for a cone constrained nonconvex optimization problem. We first establish a necessary and sufficient condition for the validity of strong duality without convexity assumptions with a possibly empty solution set of the original problem, and second, via Slater-type conditions involving quasi interior or quasirelative interior notions, various results about strong duality are also obtained. Our conditions can be used where no previous result is applicable, even in a finite dimensional or convex setting.