Planar Conjugate Gradient Algorithm for Large-Scale Unconstrained Optimization,Part 2: Application

In this paper, we describe an application of the planar conjugate gradient method introduced in Part 1 (Ref. 1) and aimed at solving indefinite nonsingular sets of linear equations. We prove that it can be used fruitfully within optimization frameworks; in particular, we present a globally convergent truncated Newton scheme, which uses the above planar method for solving the Newton equation. Finally, our approach is tested over several problems from the CUTE collection (Ref. 2).This work was supported by MIUR, FIRB Research Program on Large-Scale Nonlinear Optimization, Rome, Italy.The author acknowledges Luigi Grippo and Stefano Lucidi, who contributed considerably to the elaboration of this paper. The exchange of experiences with Massimo Roma was a constant help in the investigation. The author expresses his gratitude to the Associate Editor and the referees for suggestions and corrections.