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

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
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