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Volume 18, Issue 1
Solving Trust Region Problem in Large Scale Optimization

Bing-Sheng He

J. Comp. Math., 18 (2000), pp. 1-12.

Published online: 2000-02

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  • Abstract

This paper presents a new method for solving the basic problem in the "model-trust region" approach to large scale minimization: Compute a vector $x$ such that $1/2 x^THx +c^Tx $ = min, subject to the constraint $\| x \|_2 ≤a$. The method is a combination of the CG method and a projection and contraction (PC) method. The first (CG) method with $x_0 = 0$ as the starting point either directly offers a solution of the problem, or — as soon as the norm of the iteration is greater than $a$, — it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.

  • Keywords

Trust region problem, Conjugate gradient method, Projection and contraction method.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-18-1, author = {He , Bing-Sheng}, title = {Solving Trust Region Problem in Large Scale Optimization}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {1}, pages = {1--12}, abstract = {

This paper presents a new method for solving the basic problem in the "model-trust region" approach to large scale minimization: Compute a vector $x$ such that $1/2 x^THx +c^Tx $ = min, subject to the constraint $\| x \|_2 ≤a$. The method is a combination of the CG method and a projection and contraction (PC) method. The first (CG) method with $x_0 = 0$ as the starting point either directly offers a solution of the problem, or — as soon as the norm of the iteration is greater than $a$, — it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9018.html} }
TY - JOUR T1 - Solving Trust Region Problem in Large Scale Optimization AU - He , Bing-Sheng JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 12 PY - 2000 DA - 2000/02 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9018.html KW - Trust region problem, Conjugate gradient method, Projection and contraction method. AB -

This paper presents a new method for solving the basic problem in the "model-trust region" approach to large scale minimization: Compute a vector $x$ such that $1/2 x^THx +c^Tx $ = min, subject to the constraint $\| x \|_2 ≤a$. The method is a combination of the CG method and a projection and contraction (PC) method. The first (CG) method with $x_0 = 0$ as the starting point either directly offers a solution of the problem, or — as soon as the norm of the iteration is greater than $a$, — it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.

He , Bing-Sheng. (2000). Solving Trust Region Problem in Large Scale Optimization. Journal of Computational Mathematics. 18 (1). 1-12. doi:
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