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Mathematics of Computation

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A bench mark experiment for minimization algorithms

Author: J. N. Lyness
Journal: Math. Comp. 33 (1979), 249-264
MSC: Primary 65K05; Secondary 90C30
MathSciNet review: 514822
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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.

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  • William C. Davidon, Optimally conditioned optimization algorithms without line searches, Math. Programming 9 (1975), no. 1, 1–30. MR 383741, DOI
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  • J. N. Lyness, A bench mark experiment for minimization algorithms, Math. Comp. 33 (1979), no. 145, 249–264. MR 514822, DOI
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Keywords: Numerical software evaluation, affine scale invariance, minimization algorithms, optimization algorithms
Article copyright: © Copyright 1979 American Mathematical Society