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 c lass of trust-region-based algorithms for solving the smooth nonlinear prog ramming problem with equality constraints. The results are proved under ver y mild conditions on the quasi-normal and tangential components of the tria l steps. The Lagrange multiplier estimates and the Hessian estimates are as sumed to be bounded. No regularity assumption is made. In particular, linea r independence of the gradients of the constraints is not assumed. The theo ry 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.