A limited memory steepest descent method. / Fletcher, Roger.
In: Mathematical Programming, Vol. 135, No. 1-2, 10.2012, p. 413-436.Research output: Contribution to journal › Article
}
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 -