TY  - JOUR
T1  - A limited memory steepest descent method
A1  - Fletcher,Roger
AU  - Fletcher,Roger
PY  - 2012/10
Y1  - 2012/10
N2  - The possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the Barzilai-Borwein choice of step-size, and other related ideas. These methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems. This paper suggests a method which is able to take advantage of the availability of a few additional 'long' vectors of storage to achieve a significant improvement in performance, both for quadratic and non-quadratic objective functions. It makes use of certain Ritz values related to the Lanczos process (Lanczos in J Res Nat Bur Stand 45:255-282, 1950). Some underlying theory is provided, and numerical evidence is set out showing that the new method provides a competitive and more simple alternative to the state of the art l-BFGS limited memory method. © 2011 Springer and Mathematical Optimization Society.
AB  - The possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the Barzilai-Borwein choice of step-size, and other related ideas. These methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems. This paper suggests a method which is able to take advantage of the availability of a few additional 'long' vectors of storage to achieve a significant improvement in performance, both for quadratic and non-quadratic objective functions. It makes use of certain Ritz values related to the Lanczos process (Lanczos in J Res Nat Bur Stand 45:255-282, 1950). Some underlying theory is provided, and numerical evidence is set out showing that the new method provides a competitive and more simple alternative to the state of the art l-BFGS limited memory method. © 2011 Springer and Mathematical Optimization Society.
U2  - 10.1007/s10107-011-0479-6
DO  - 10.1007/s10107-011-0479-6
M1  - Article
JO  - Mathematical Programming
JF  - Mathematical Programming
SN  - 0025-5610
IS  - 1-2
VL  - 135
SP  - 413
EP  - 436
ER  -