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

@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.