Abstract In this paper, a class of nonsmooth multi-objective programming problems is studied. By using generalized Farkas lemma and scalarization of multi-objective function, the optimality conditions of cone weakly efficient solution are given for the problem of minimizing a multi-objective function, where the multi-objective function is the sum of a differentiable multi-objective function and a cone convex multi-objective function, subject to a set of differentiable nonlinear functions with a controlled cone on a convex subset of a finite dimensional Euclidean space, under the conditions similar to the Abadie constraint qualification.
ZHOU Xuan-wei. Optimality conditions for a class of nonsmooth multi-objective programming problems. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 63-72.
