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

2024/05/19 by Vsevolod I. Ivanov, Ivanov, Vsevolod I.
Mathematics · Computer Science · Engineering · #Advanced Optimization Algorithms Research #Optimization and Variational Analysis #Aerospace Engineering and Control Systems

paper · pdf · doi:10.48550/arxiv.2405.11593

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.

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