Preconditioned spectral gradient method

Abstract

The spectral gradient method is a nonmonotone gradient method for large-scale unconstrained minimization. We strengthen the algorithm by modifications which globalize the method and present strategies to apply preconditioning techniques. The modified algorithm replaces a condition of uniform positive definitness of the preconditioning matrices, with mild conditions on the search directions. The result is a robust algorithm which is effective on very large problems. Encouraging numerical experiments are presented for a variety of standard test problems, for solving nonlinear Poisson-type equations, an also for finding molecular conformations by distance geometry.