A new concept of an exact auxiliary function (EAF) is introduced. A function is said to be EAF, if the set of global minimizers of this function coincides with the global solution set of the initial optimization problem. Sufficient conditions for exact equivalence of the constrained minimization problem and minimization of EAF are provided. The paper presents various classes of EAF for a non linear programming problem, which has a saddle point of Lagra ge function.