A global convergence theory for Dennis, El-Alem, and Maciel's class of trust-region algorithms for constrained optimization without assuming regularity
M. El-alem, A global convergence theory for Dennis, El-Alem, and Maciel's class of trust-region algorithms for constrained optimization without assuming regularity, SIAM J OPTI, 9(4), 1999, pp. 965-990
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.