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Sufficiency and Wolfe Type Duality for Nonsmooth Multiobjective Programming Problems
College of Science, Xi’an Shiyou University, Xi’an, China
College of Science, Xi’an University of Science and Technology, Xi’an, China
- 1 College of Science, Xi’an Shiyou University, Xi’an, China
- 2 College of Science, Xi’an University of Science and Technology, Xi’an, China
Advances in Pure Mathematics·Volume 08 (2018)·Pages 755–763·Published 6 August 2018·DOI10.4236/apm.2018.88045
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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.
KeywordsMultiobjective ProgrammingOptimality ConditionLocally Lipschitz FunctionWolfe Type Dual Problem
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