Volume 41, Number 1, January-March 2007
|Page(s)||105 - 121|
|Published online||15 June 2007|
Convergence analysis of adaptive trust region methods
College of Operations Research and Management,
Qufu Normal University, Rizhao, Shandong 276826, P.R. China, and
Department of Computer & Information Science, University of
Michigan-Dearborn, Michigan MI48128, USA; email@example.com or firstname.lastname@example.org
2 Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2734, Beijing 100080, P.R. China; email@example.com
3 Department of Computer & Information Science, University of Michigan-Dearborn, Michigan MI48128, USA; firstname.lastname@example.org
Accepted: 16 October 2006
In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the objective function are more consistent at the current iterate. The global convergence, super-linear and quadratic convergence rate are analyzed under some mild conditions. Numerical results show that some special adaptive trust region methods are available and efficient in practical computation.
Mathematics Subject Classification: 90C30 / 49M37 / 65K05
Key words: Adaptive trust region method / unconstrained optimization / global convergence / super-linear convergence.
© EDP Sciences, ROADEF, SMAI, 2007
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