A bench mark experiment for minimization algorithms

Lyness, J. N.

doi:10.1090/S0025-5718-1979-0514822-7

A bench mark experiment for minimization algorithms
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by J. N. Lyness PDF

Math. Comp. 33 (1979), 249-264 Request permission

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 ${g_Q}({X_1})$. 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.

References

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A Fortran Implementation of Davidon’s Optimally Conditioned Method

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Subroutine

A Quasi-Newton Algorithm to Find the Unconstrained Minimum of a Function of N Variables When First Derivatives are Available

J. N. Lyness, A bench mark experiment for minimization algorithms, Math. Comp. 33 (1979), no. 145, 249–264. MR 514822, DOI 10.1090/S0025-5718-1979-0514822-7

A Pilot Scheme for Minimization Software Evaluation

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) SIAM-AMS Proc., Vol. IX, Amer. Math. Soc., Providence, R.I., 1976, pp. 53–72. MR 0426428