First and Second Order Necessary and Sufficient Optimality Conditions of Fritz John Type for Vector Problems over Cones

Abstract

In this paper, we obtain a new proof of Fritz John necessary optimality conditions for vector problems applying Kakutani fixed point theorem and Hadamard directional derivative. We also derive a similar proof of second-order Fritz John necessary optimality conditions. Sufficient conditions for weak global efficiency with generalized convex functions and local efficiency are provided.

arXiv comment12 pages