(untitled) (Journal of Computational Mathematics, 2000)
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.