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arXiv · 1710.03989

Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions

Yi-Bin Xiao·Nguyen Van Tuyen·Ching-Feng Wen·Jen-Chih Yao
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Abstract

In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some second-order constraint qualifications of Zangwill type, Abadie type and Mangasarian~--~Fromovitz type as well as a regularity condition of Abadie type are proposed in a nonsmooth setting. The connections between these proposed conditions are established. They are applied to develop second-order Karush--Kuhn--Tucker necessary optimality conditions for local (weak, Geoffrion properly) efficient solutions to the considered problem. Examples are also given to illustrate the obtained results.

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Yi-Bin Xiao, Nguyen Van Tuyen, Ching-Feng Wen, Jen-Chih Yao. 2017-10-11. Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions. https://arxiv.org/abs/1710.03989

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