Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters

A model algorithm based on the successive quadratic programming method for solving the general nonlinear programming problem is presented. The objecti ve function and the constraints of the problem are only required to be diff erentiable and their gradients to satisfy a Lipschitz condition. The strategy for obtaining global convergence is based on the trust region approach. The merit function is a type of augmented Lagrangian. A new updat ing scheme is introduced for the penalty parameter, by means of which monot one increase is not necessary. Global convergence results are proved and numerical experiments are present ed.