Taiwanese Journal of Mathematics


Xian-Jun Long and Nan-Jing Huang

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In this paper, a nonsmooth multiobjective programming problem is introduced and studied. By using the generalized Guignard constraint qualification, some stronger Kuhn-Tucker type necessary optimality conditions for efficiency in terms of convexificators are established, in which we are not assuming that the objective functions are directionally differentiable. Moreover, some conditions which ensure that a feasible solution is an efficient solution to nonsmooth multiobjective programming problems are also given. The results presented in this paper improve the corresponding results in the literature.

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Taiwanese J. Math., Volume 18, Number 3 (2014), 687-699.

First available in Project Euclid: 10 July 2017

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Zentralblatt MATH identifier

Primary: 90C29: Multi-objective and goal programming 90C46: Optimality conditions, duality [See also 49N15] 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56]

optimality condition nonsmooth multiobjective programming efficient solution Dini directional derivatives convexificators constraint qualification


Long, Xian-Jun; Huang, Nan-Jing. OPTIMALITY CONDITIONS FOR EFFICIENCY ON NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS. Taiwanese J. Math. 18 (2014), no. 3, 687--699. doi:10.11650/tjm.18.2014.3730. https://projecteuclid.org/euclid.twjm/1499706434

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