On the Convergence Theory of Trust-Region-Based Algorithms for Equality-Constrained Optimization

In a recent paper, Dennis, El{Alem, and Maciel proved global convergence to a stationary point for a general trust{region{based algorithm for equality{constrained optimization. This general algorithm is based on appropriate choices of trust{region subproblems and seems particularly suitable for large problems. This paper shows global convergence to a point satisfying the second{order necessary optimality conditions for the same general trust{region{based algorithm. The results given here can be seen as a generalization of the convergence results for trust{regions methods for unconstrained optimization obtained by Mor e and Sorensen. The behavior of the trust radius and the local rate of convergence are analyzed. Some interesting facts concerning the trust{region subproblem for the linearized constraints, the quasi{normal component of the step, and the hard case are presented. It is shown how these results can be applied to a class of discretized optimal control problems.