Nondifferentiable mathematical programming involving
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-2012-256Published: 1 November 2012
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.