A spectral conjugate gradient method for unconstrained optimization. (English) Zbl 0990.90134

Birgin, E. G.; Martínez, J. M.

Appl. Math. Optimization 43, No. 2, 117-128 (2001).

Summary: A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak-Ribière and the Fletcher-Reeves formulae are compared using a spectral scaling derived from Raydan’s spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in optics is presented.

MSC:

90C52	Methods of reduced gradient type
90C30	Nonlinear programming
65K05	Numerical mathematical programming methods

Keywords:

spectral gradient method; scaled conjugate gradient algorithms; large-scale unconstrained minimization