A bench mark experiment for minimization algorithms
Author:
J. N. Lyness
Journal:
Math. Comp. 33 (1979), 249264
MSC:
Primary 65K05; Secondary 90C30
MathSciNet review:
514822
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: In this paper we suggest a single bench mark problem family for use in evaluating unconstrained minimization algorithms or routines. In essence, this problem consists of measuring, for each algorithm, the rate at which it descends an unlimited helical valley. The periodic nature of the problem allows us to exploit affine scale invariance properties of the algorithm. As a result, the capacity of the algorithm to minimize a wide range of helical valleys of various scales may be summarized by calculating a single valued function . The measurement of this function is not difficult, and the result provides information of a simple, general character for use in decisions about choice of algorithm.
 [W]
William
C. Davidon, Optimally conditioned optimization algorithms without
line searches, Math. Programming 9 (1975),
no. 1, 1–30. MR 0383741
(52 #4621)
 [W]
C. DAVIDON & L. NAZARETH (1977), DRVOCRA Fortran Implementation of Davidon's Optimally Conditioned Method, ANLAMD Technical Memorandum No. 306.
 [R]
FLETCHER (1972), "Conjugate direction methods," Numerical Methods for Unconstrained Optimization, (W. Murray, Editor), Academic Press, London, pp. 7386.
 [P]
E. GILL, W. MURRAY, S. M. PICKEN, S. R. GRAHAM & M. H. WRIGHT (1975), Subroutine QNMDER, A QuasiNewton Algorithm to Find the Unconstrained Minimum of a Function of N Variables When First Derivatives are Available, Technical Memorandum E4/02/0/Fortran/11/75, National Physical Laboratory, Teddington, Middlesex TW11 OLW, England.
 [J]
J.
N. Lyness, The affine scale invariance of
minimization algorithms, Math. Comp.
33 (1979), no. 145, 265–287. MR 514823
(80m:65050b), http://dx.doi.org/10.1090/S00255718197905148239
 [J]
N. LYNESS & C. GREENWELL (1977), A Pilot Scheme for Minimization Software Evaluation, ANLAMD Technical Memorandum No. 323.
 [M]
M.
J. D. Powell, Some global convergence properties of a variable
metric algorithm for minimization without exact line searches,
Nonlinear programming (Proc. Sympos., New York, 1975) Amer. Math. Soc.,
Providence, R. I., 1976, pp. 53–72. SIAMAMS Proc., Vol. IX. MR 0426428
(54 #14371)
 [W]
 C. DAVIDON (1975), "Optimally conditioned optimization algorithms without line searches", Math. Programming, v. 9, pp. 130. MR 0383741 (52:4621)
 [W]
 C. DAVIDON & L. NAZARETH (1977), DRVOCRA Fortran Implementation of Davidon's Optimally Conditioned Method, ANLAMD Technical Memorandum No. 306.
 [R]
 FLETCHER (1972), "Conjugate direction methods," Numerical Methods for Unconstrained Optimization, (W. Murray, Editor), Academic Press, London, pp. 7386.
 [P]
 E. GILL, W. MURRAY, S. M. PICKEN, S. R. GRAHAM & M. H. WRIGHT (1975), Subroutine QNMDER, A QuasiNewton Algorithm to Find the Unconstrained Minimum of a Function of N Variables When First Derivatives are Available, Technical Memorandum E4/02/0/Fortran/11/75, National Physical Laboratory, Teddington, Middlesex TW11 OLW, England.
 [J]
 N. LYNESS (1979), "The affine scale invariance of minimization algorithms," Math. Comp., v. 33, pp. 265287. MR 514823 (80m:65050b)
 [J]
 N. LYNESS & C. GREENWELL (1977), A Pilot Scheme for Minimization Software Evaluation, ANLAMD Technical Memorandum No. 323.
 [M]
 J. D. POWELL (1975), Some Global Convergence Properties of a Variable Metric Algorithm for Minimization Without Exact Line Searches, Technical Memorandum C. S. S. 15, AERE Harwell. MR 0426428 (54:14371)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65K05,
90C30
Retrieve articles in all journals
with MSC:
65K05,
90C30
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905148227
PII:
S 00255718(1979)05148227
Keywords:
Numerical software evaluation,
affine scale invariance,
minimization algorithms,
optimization algorithms
Article copyright:
© Copyright 1979
American Mathematical Society
