On convergence properties of the modified trust region method under Hölderian error bound condition

<p style='text-indent:20px;'>Trust region method is one of the important methods for nonlinear equations. In this paper, we show that the modified trust region method converges globally under the Hölderian continuity of the Jacobian. The convergence order of the method is also given under the Hölderian error bound condition.</p>

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Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

Computational Optimization and Applications ◽

10.1007/s10589-005-3078-8 ◽

2006 ◽

Vol 34 (2) ◽

pp. 215-227 ◽

Cited By ~ 34

Author(s):

Jinyan Fan

Keyword(s):

Convergence Rate ◽

Error Bound ◽

Nonlinear Equations ◽

Trust Region Method ◽

Trust Region ◽

Local Error ◽

Local Error Bound ◽

Region Method ◽

Local Error Bound Condition

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A BFGS trust-region method for nonlinear equations

Computing ◽

10.1007/s00607-011-0146-z ◽

2011 ◽

Vol 92 (4) ◽

pp. 317-333 ◽

Cited By ~ 43

Author(s):

Gonglin Yuan ◽

Zengxin Wei ◽

Xiwen Lu

Keyword(s):

Nonlinear Equations ◽

Trust Region Method ◽

Trust Region ◽

Region Method

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A new self-adaptive trust region method for unconstrained optimization

Journal of Vibration and Control ◽

10.1177/1077546311408473 ◽

2011 ◽

Vol 18 (9) ◽

pp. 1303-1309 ◽

Cited By ~ 1

Author(s):

Zhaocheng Cui ◽

Boying Wu

Keyword(s):

Unconstrained Optimization ◽

Superlinear Convergence ◽

Optimization Problems ◽

Trust Region Method ◽

Trust Region ◽

Convergence Properties ◽

Region Method ◽

Unconstrained Optimization Problems ◽

Global And Superlinear Convergence ◽

Self Adaptive

In this paper, we propose a new self-adaptive trust region method for unconstrained optimization problems and develop some convergence properties. In our algorithm, we use the previous and current iterative information to define a suitable trust region radius at each iteration. The global and superlinear convergence properties of the algorithm are established under reasonable assumptions. Preliminary numerical results show that the new method is efficient and attractive for solving unconstrained optimization problems.

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A Nonmonotone Adaptive Trust Region Method Based on Conic Model for Unconstrained Optimization

Journal of Optimization ◽

10.1155/2014/237279 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

Zhaocheng Cui

Keyword(s):

Unconstrained Optimization ◽

Optimization Problems ◽

Trust Region Method ◽

Trust Region ◽

New Method ◽

Convergence Properties ◽

Initial Trust ◽

Conic Model ◽

Region Method ◽

Unconstrained Optimization Problems

We propose a nonmonotone adaptive trust region method for unconstrained optimization problems which combines a conic model and a new update rule for adjusting the trust region radius. Unlike the traditional adaptive trust region methods, the subproblem of the new method is the conic minimization subproblem. Moreover, at each iteration, we use the last and the current iterative information to define a suitable initial trust region radius. The global and superlinear convergence properties of the proposed method are established under reasonable conditions. Numerical results show that the new method is efficient and attractive for unconstrained optimization problems.

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