In this paper, a quasidifferentiable programming problem with inequality constraints is considered. Firs, a general form of optimality conditions for this problem is given, which contains the results of luderer, Kuntz and Scholtes. Next, a new genralized K-T condition is derived. The new optimality condition doesn't use luderer's regularity assumption and its Lagrangian multipliers don't depend on he particualr elements in the superdifferentials of the object function and constrain functions. Finally, a penalty function for the problem is studied. Sufficient conditions of the object function and constraint functions. Finally, a penalty function for the problem is studied. Sufficient conditions of he penalty function attaining a global minimum are obtained.
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