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

Bing Sheng He

DOI:

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 \le 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 start point either directly offers a solution of the problem, or -- as soon as the norm of the iterate 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 andcontraction method

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@Article{JCM-18-1, author = {}, 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 \le 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 start point either directly offers a solution of the problem, or -- as soon as the norm of the iterate 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 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 KW - Conjugate gradient method KW - Projection andcontraction 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 \le 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 start point either directly offers a solution of the problem, or -- as soon as the norm of the iterate 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.
Bing Sheng He. (1970). Solving Trust Region Problem in Large Scale Optimization. Journal of Computational Mathematics. 18 (1). 1-12. doi:
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