The convergence of subspace trust region methods

✍ Scribed by Zhen-Jun Shi; Zhiwei Xu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 664 KB
• Volume: 231
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.02.100

✦ Synopsis

a b s t r a c t

The trust region method is an effective approach for solving optimization problems due to its robustness and strong convergence. However, the subproblem in the trust region method is difficult or time-consuming to solve in practical computation, especially in largescale problems. In this paper we consider a new class of trust region methods, specifically subspace trust region methods. The subproblem in these methods has an adequate initial trust region radius and can be solved in a simple subspace. It is easier to solve than the original subproblem because the dimension of the subproblem in the subspace is reduced substantially. We investigate the global convergence and convergence rate of these methods.