Sufficiency and Wolfe Type Duality for Nonsmooth Multiobjective Programming Problems - Advances in Pure Mathematics

APM > Vol.8 No.8, August 2018

Sufficiency and Wolfe Type Duality for Nonsmooth Multiobjective Programming Problems ()

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Download as PDF (Size: 451KB) PP. 755-763

DOI: 10.4236/apm.2018.88045 762 Downloads 1,444 Views Citations

Author(s)

Gang An¹, Xiaoyan Gao²

Affiliation(s)

¹College of Science, Xi’an Shiyou University, Xi’an, China.
²College of Science, Xi’an University of Science and Technology, Xi’an, China.

ABSTRACT

In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order

type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model.

KEYWORDS

Multiobjective Programming, Optimality Condition, Locally Lipschitz Function, Wolfe Type Dual Problem

Share and Cite:

An, G. and Gao, X. (2018) Sufficiency and Wolfe Type Duality for Nonsmooth Multiobjective Programming Problems. Advances in Pure Mathematics, 8, 755-763. doi: 10.4236/apm.2018.88045.

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