Systematic Approach for Comparing the Computational Speed of Unconstrained Minimization Algorithms
The comparison of mathematical programming algorithms is inherently difficult, especially when deriving general conclusions about the relative usefulness, applicability, and efficiency of different algorithms. The problem is complicated by the variety of approaches used to compare algorithms. Most often, some approaches ignore essential aspects of the comparison or fail to provide sufficient information about the following items: (a) clarification of the objectives of the comparison; (b) clear and complete description of the algorithms being compared; (c) specification of the memory requirements; (d) use of the same experimental conditions for all of the algorithms being compared; (e) sufficient information about the experimental conditions and the numerical results, so as to make them easily reproducible; (f) use of enough performance indexes to ensure the fulfillment of the objectives of the comparison; (g) use of a reasonably large set of test problems having different characteristics; (h) clarification of the way in which the derivatives are computed; (i) measurement of the computational speed; (j) measurement of the effect of the stopping conditions; (k) measurement of the sensitivity to scaling; (l) presentation of the convergence rates; (m) use of several nominal points for each test problem; and (n) use of a standard format to present the result of the comparison.
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