Taiwanese Journal of Mathematics

OPTIMALITY CONDITIONS FOR EFFICIENCY ON NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS

Xian-Jun Long and Nan-Jing Huang

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706434

Digital Object Identifier
doi:10.11650/tjm.18.2014.3730

Mathematical Reviews number (MathSciNet)
MR3213380

Zentralblatt MATH identifier
1357.90133

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

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

Citation

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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