A global convergence theory for Dennis, El-Alem, and Maciel's class of trust-region algorithms for constrained optimization without assuming regularity

This work presents a convergence theory for Dennis, El-Alem, and Maciel's 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. No regularity assumption is made. In particular, 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 satisfies one of four types of Mayer-Bliss stationary conditions in the limit.