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

Vsevolod I. Ivanov

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arXiv · 2405.11593

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

Vsevolod I. Ivanov

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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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Vsevolod I. Ivanov. 2024-05-19. First and Second Order Necessary and Sufficient Optimality Conditions of Fritz John Type for Vector Problems over Cones. https://arxiv.org/abs/2405.11593

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