J. Comp. Math., Volume 18.

Solving Trust Region Problem In Large Scale Optimization

Bing Sheng He 1

1 Department of Mathematics, Nanjing University, Naming 210093, China


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.

Key words: Trust region problem; Conjugate gradient method; Projection andcontraction method.


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