Research
Nondifferentiable mathematical programming involving (
G
,
β
)
1 Department of Math., Hanshan Normal University, Chaozhou, Guangdong, 521041, China
2 Department of Comp. Tech., Hanshan Normal University, Chaozhou, Guangdong, 521041, China
Journal of Inequalities and Applications 2012, 2012:256 doi:10.1186/1029-242X-2012-256
Published: 1 November 2012Abstract
In this paper, we define new vector generalized convexity, namely nondifferentiable
vector 
-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.
Keywords:
-invexity; G-Karush-Kuhn-Tucker sufficient optimality conditions; G-Karush-Kuhn-Tucker necessary optimality conditions; duality
