Preconditioned Spectral Gradient Method

  title={Preconditioned Spectral Gradient Method},
  author={Francisco Luengo and Marcos Raydan and William Kile Glunt and Tom L. Hayden},
  journal={Numerical Algorithms},
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… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 32 references

Solution of nonlinear Poisson-type equations, Appl

B. M. Averick, J. M. Ortega
Numer. Math • 1991
View 6 Excerpts
Highly Influenced

A nonmonotone line search technique for Newton’s method

L. Grippo, F. Lampariello, S. Lucidi
SIAM J. Numer. Anal • 1986
View 4 Excerpts
Highly Influenced

Finite Element Solution of Boundary Value Problems, Theory and Computation

O. Axelsson, V. A. Barker
View 2 Excerpts
Highly Influenced

A spectral conjugate gradient method for unconstrained optimization

E. G. Birgin, J. M. Martínez
Appl. Math. Optim • 2001
View 1 Excerpt

Determination of thickness and optical constants of a - Si : H films from transmittance data

M. Mulato, I. Chambouleyron, E. G. Birgin, J. M. Martínez
Appl . Phys . Lett . • 2000

Determination of thickness and optical constants of a-Si:H films from transmittance data, Appl

M. Mulato, I. Chambouleyron, E. G. Birgin, J. M. Martínez
Phys. Lett • 2000

Low cost optimization techniques for solving the nonlinear seismic reflection tomography

Z. Castillo, D. Cores, M. Raydan
problem, Optim. Engrg • 2000