@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 = {<p style="text-align: justify;">This paper presents a new method for solving the basic problem in the &quot;model-trust region&quot; 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.</p>},
issn = {1991-7139},
doi = {https://doi.org/2000-JCM-9018},
url = {https://global-sci.com/article/85525/solving-trust-region-problem-in-large-scale-optimization}
}