CURVILINEAR STABILIZATION TECHNIQUES FOR TRUNCATED NEWTON METHODS IN LARGE-SCALE UNCONSTRAINED OPTIMIZATION

The aim of this paper is to define a new class of minimization algorit hms for solving large scale unconstrained problems. In particular we d escribe a stabilization framework, based on a curvilinear linesearch, which uses a combination of a Newton-type direction and a negative cur vature direction. The motivation for using negative curvature directio n is that of taking into account local nonconvexity of the objective f unction. On the basis of this framework, we propose an algorithm which uses the Lanczos method for determining at each iteration both a Newt on-type direction and an effective negative curvature direction. The r esults of extensive numerical testing are reported together with a com parison with the LANCELOT package. These results show that the algorit hm is very competitive, which seems to indicate that the proposed appr oach is promising.