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Vietnam Journal of Mathematics 40:2&3(2012)
275-284
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Optimality Conditions of the G-Type in Locally
Lipschitz Multiobjective Programming
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Young Min Kang1, Do Sang Kim1
and Moon Hee Kim2
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1Department
of Applied Mathematics, Pukyong National University,
Busan 608-737, Korea
2School of Free Major, Tongmyong University,
Busan 608-711, Korea
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Dedicated to Professor
Phan Quoc Khanh on the occasion of his 65th birthday
Received November 25,
2011
Revised May 7, 2012
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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.
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2000 Mathematics
Subject Classification. 90C46, 90C26.
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Keywords.
Locally Lipschitz function, G-invex
function, G-Fritz John necessary
optimality condition, G-Karush-Kuhn-Tucker
necessary optimality condition.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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