Exact Penalty Functions a Lower Bound to the Penalty Parameter

We consider a class of nondifferentiable penalty functions associated to nonlinear programming problem with equality and inequality cons-traints. We analyze the relationships between the solutions of the cons-trained problem and the solutions of the penalty function. Assuming first-order sufficient optimality condition of the constrained problem, we show the exactness of the class of penalty functions and give an estimative of the size of the exact penalty parameter. Moreover, under assumption, exactness of the penalty function, we provide a lower bound to the penalty parameter in terms of the Lagrange multipliers of the nonlinear programming problem