ON THE CONVERGENCE THEORY OF TRUST-REGION-BASED ALGORITHMS FOR EQUALITY-CONSTRAINED OPTIMIZATION

In a recent paper, Dennis, El-Alem, and Maciel proved global convergen ce to a stationary point for a general trust-region-based algorithm fo r equality-constrained optimization. This general algorithm is based o n appropriate choices of trust-region subproblems and seems particular ly suitable for large problems. This paper shows global convergence to a point satisfying the second-order necessary optimality conditions f or the same general trust-region-based algorithm. The results given he re can be seen as a generalization of the convergence results for trus t-regions methods for unconstrained optimization obtained by More and Sorensen. The behavior of the trust radius and the local rate of conve rgence are analyzed. Some interesting facts concerning the trust-regio n subproblem for the linearized constraints, the quasi-normal componen t 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 probl ems.