Optimality and duality for nonsmooth multiobjective programming using G-type I functions

摘要

In this paper, (generalized) G-type I functions are defined for a nonlinear multiobjective programming problem where the functions involved are assumed to be locally Lipschitz. This new class of functions is a generalization of G-invex functions defined in Kang et al. (2012) [20]. Examples are given to show the existence of these functions. G-type Kuhn–Tucker necessary conditions are established for a nondifferentiable multiobjective programming problem (GMP). By using suitable G-type I functions, sufficient optimality conditions are derived for the problem (GMP). Further a Mond–Weir type dual (GMWD) is formulated and using these newly defined functions various duality results are established.