A bench mark experiment for minimization algorithms
James N. Lyness · Mathematics of Computation · 1979
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 ) {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.