Optimality conditions for nonsmooth multiobjective programming
2008
This paper considers the following nonsmooth multiobjective programming problem: (P) weak min f(x)=(f 1 (x), hellip, f p (x)), s.t. -g(x)isinS, h(x)=0, where xisinR n , 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.
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