Author:
Yuan Dehui,Liu Xiaoling,Yang Shengyun,Lai Guoming
Abstract
Abstract
In this paper, we define new vector generalized convexity, namely nondifferentiable vector
(
G
f
,
β
f
)
-invexity, for a given locally Lipschitz vector function f. Basing on this new nondifferentiable vector generalized invexity, we have managed to deal with nondifferentiable nonlinear programming problems under some assumptions. Firstly, we present G-Karush-Kuhn-Tucker necessary optimality conditions for nonsmooth mathematical programming problems. With the new vector generalized invexity assumption, we also obtain G-Karush-Kuhn-Tucker sufficient optimality conditions for the same programming problems. Moreover, we establish duality results for this kind of multiobjective programming problems. In the end, a suitable example illustrates that the new optimality results are more useful for some class of optimization problems than the optimality conditions with invex functions.
MSC:90C26.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
2 articles.
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