An Adaptive Descent Extension of the Polak-Rebière-Polyak Conjugate Gradient Method Based on the Concept of Maximum Magnification

Recently, a one-parameter extension of the Polak-Rebière-Polyak (PRP) conjugate gradient (CG) method has been suggested, having acceptable theoretical features and promising numerical behavior. Here, based on an eigenvalue analysis on the method in the sense of avoiding a search direction in the direction of the maximum magnification by a symmetric version of the search direction matrix, an adaptive formula for computing parameter of the method is proposed. Under standard assumptions, the given formula ensures the sufficient descent property and guarantees the global convergence of the method. Numerical experiments are done on a set of CUTEr test problems. They show practical effectiveness of the suggested formula for the parameter of the method

Keywords:

Nonlinear programming , Unconstrained optimization , Conjugate gradient method , Maximum magnification , Line search.