The Penalty Funkcions Method and Optimality Conditons

The presented work is devoted to one of the most important areas of applied mathematics, namely mathematical programming. The following general mathematical programming problem is considered where are Lipschitz, and is closed set. The purpose of the work is to obtain optimality conditions for the problem posed using the method of penalty functions. The obtained necessary conditions are expressed in the language of subdifferentials, which are a generalization of the method of indefinite Lagrange coefficients for nonsmooth optimization problems.