Solving Trust Region Problem In Large Scale Optimization
Bing Sheng He 11 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.