A Global Convergence Theory for a General Class ofTrust - Region - Based Algorithms for Constrained OptimizationWithout Assuming Regularity

This work presents a convergence theory for a general class of trust-region-based algorithms for solving the smooth nonlinear programming problem with equality constraints. The results are proved under very mild conditions on the quasi-normal and tangential components of the trial steps. The Lagrange multiplier estimates and the Hessian estimates are assumed to be bounded. In addition, the regularity assumption is not made. In particular, the linear independence of the gradients of the constraints is not assumed. The theory proves global convergence for the class. In particular, it shows that a subsequence of the iteration sequence satisses one of four types of Mayer-Bliss stationary conditions in the limit. This theory holds for Dennis, El-Alem, and Maciel's class of trust-region-based algorithms.