Year: 2000
Author: Bing-Sheng He
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2000-JCM-9018
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 1 : pp. 1–12
Published online: 2000-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Trust region problem Conjugate gradient method Projection and contraction method.