Optimality conditions for nonsmmoth mixed programming with approximate Jacobian

It is shown that optimality conditions for multiobjective programming problems involving inequality, equality and set constraint are hold, by using approximate Jacobian. Also it is one of the chief reasons behind the development of smaller convex-valued subdifferentials such as those introduced by Clarke and Michel-Penot and nonconvex subdifferentials such as those studied by Modukhovich andTreiman.

کلیدواژه ها:

Approximate Jacobian ، Locally Lipschitz functions ، Dini derivative ، Necessary optimalityconditions. Nonsmooth optimizations