Fabián Flores-Bazán, Giandomenico Mastroeni:
Characterizing FJ and KKT conditions in nonconvex mathematical programming with applications
In this paper we analyse the Fritz John and Karush-Kuhn-Tucker conditions for a (Gateaux) differentiable nonconvex optimization problem with inequality constraints and a geometric constraint set. Fritz John condition is characterized in terms of an alternative theorem which covers beyond standard situations; while characterizations of KKT conditions, without assuming constraints qualifications, are related to strong duality of a suitable linear approximation of the given problem and the properties of its associated image mapping. Several examples are exhibited showing the usefulness and optimality, in a certain sense, of our results, which even provide much more information than those (including Mordukhovich normal cone or Clarke
This preprint gave rise to the following definitive publication(s):
Fabián FLORES-BAZáN, Giandomenico MASTROENI: Characterizing FJ and KKT conditions in nonconvex mathematical programming with applications. SIAM Journal on Optimization, vol. 25, 1, pp. 647-676, (2015).