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Vietnam Journal of Mathematics 40:2&3(2012) 275-284

 

Optimality Conditions of the G-Type in Locally

Lipschitz Multiobjective Programming

Young Min Kang1, Do Sang Kim1 and Moon Hee Kim2

1Department of Applied Mathematics, Pukyong National University,

Busan 608-737, Korea

2School of Free Major, Tongmyong University, Busan 608-711, Korea

Dedicated to Professor Phan Quoc Khanh on the occasion of his 65th birthday

Received November 25, 2011

Revised May 7, 2012

Abstract. In this paper, we extend the Antczak definition of G-invexity for differentiable functions to the case of locally Lipschitz functions. We establish G-Fritz John and G-Karush-Kuhn-Tucker necessary optimality conditions for locally Lipschitz multiobjective programming. Our optimality conditions extend the results of Antczak to the locally Lipschitz multiobjective programming.

2000 Mathematics Subject Classification. 90C46, 90C26.

Keywords. Locally Lipschitz function, G-invex function, G-Fritz John necessary optimality condition, G-Karush-Kuhn-Tucker necessary optimality condition.

 

 

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