Resumen de Augmented penalty algorithms based on BFGS secant approximations and trust regions

Graciela M. Croceri, Graciela N. Sottosanto, María Cristina Maciel

• An iterative method for solving the nonlinear minimization problem with equality constraints is presented. The method is based on the sequential minimization of the augmented Lagrangian function. The unconstrained minimization subproblems are solved by using a technique based on the conjugate gradients combined with the trust region approach as globalization strategy. The Hessian matrix of the augmented Lagrangian is updated by using a BFGS-like structured secant approximation. Global convergence results are shown. The method is applied to solve the equality constrained nonlinear least squares problem. Numerical results are presented not only with well-known test problems but also with ill-posed problems involving a regularization. Even though the tested problems are small and medium, features like the conjugate gradient/trust region strategy and the structured secant approximation make the proposed algorithm specially efficient for large scale problems.