Globally convergent Newton methods for constrained optimization using differentiable exact penalty functions

In this paper we consider Newton´s method for solving the system of necessary optimality conditions of optimization problems with equality and inequality constraints. The principal drawbacks of the method are the need for a good starting point, the inability to distinguish between local maxima and local minima, and, when inequality constraints are present, the necessity to solve a quadratic programming problem at each interation. We show that all these drawbacks can be overcome to a great extent without sacrificing the superlinear convergence rate by making use of exact differentiable penalty functions introduced by Di Pillo and Grippo [1]. We also demonstrate a close relationship between the class of penalty functions of Di Pillo and Grippo and the class of Fletcher [12].