Article ID: | iaor1991716 |
Country: | Netherlands |
Volume: | 47 |
Issue: | 3 |
Start Page Number: | 305 |
End Page Number: | 336 |
Publication Date: | Aug 1990 |
Journal: | Mathematical Programming (Series A) |
Authors: | Burke James V., Mor Jorge J., Toraldo Gerardo |
The authors develop a convergence theory for convex and linearly constrained trust region methods which only requires that the step between iterates produce a sufficient reduction in the trust region subproblem. Global convergence is established for general convex constraints while the local analysis is for linearly constrained problems. The main local result establishes that if the sequence converges to a nondegenerate stationary point then the active constraints at the solution are identified in a finite number of iterations. As a consequence of the identification properties, the authors develop rate of convergence results by assuming that the step is a truncated Newton method. The present development is mainly geometrical; this approach allows the development of a convergence theory without any linear independence assumptions.