This paper considers the following nonsmooth multiobjective progrmming problem: (P) Weak min f(x) = (f1(x),…, fp(x)),s.t.- g(x) ∈ S, h(x) = 0, where x ∈ R^n, f(x) ∈ R^p, g(x) ∈ R^m, h(x) ∈ R', S\subset R^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.

This paper considers the following nonsmooth multiobjective progrmming problem: (P) Weak min f(x) = (f1(x),…, fp(x)),s.t.- g(x) ∈ S, h(x) = 0, where x ∈ R^n, f(x) ∈ R^p, g(x) ∈ R^m, h(x) ∈ R', S\subset R^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.