Optimality conditions for nonsmooth multiobjective programming

This paper considers the following nonsmooth multiobjective programming problem: (P) weak min f(x)=(f₁(x), hellip, f_p(x)), s.t. -g(x)isinS, h(x)=0, where xisinRⁿ, f(x)isinR^p, g(x)isinR^m, h(x)isinR^r, SsubR^m is a closed convex cone with interior, and f, g, h satisfy the local Lipschitz condition. The necessary Lagrangian condition is established for a weak minimum of (P), and the proof is different from the proofs given by B.D.Craven, Ying Meiqian and other authors. Necessary conditions of Kuhn-Tucker type are obtained and sufficient conditions are discussed.