The regularization of a nonlinear program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. In this talk, we show that the regularization is exact if and only if the Lagrangian function of a certain selection problem has a saddle point. Moreover, the regularization parameter threshold is inversely related to the Lagrange multiplier associated with the saddle point. Our results not only provide a fresh perspective on exact regularization but also extend the main results of Friedlander and Tseng [2] on a characterization of exact regularization of a convex program to that of a nonlinear (not necessarily convex) program. We also examine inner-connections among exact regularization, exact penalization of nonlinear programs and the existence of a weak sharp minimum for certain associated nonlinear programs.
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