Nondifferentiable mathematical programming involving "Equation missing" -invexity
Dehui Yuan, Xiaoling Liu, Shengyun Yang, Guoming Lai · Journal of Inequalities and Applications · 2012
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.