Abstract
In this Presentation, we consider the minimization of a function f = f(x), where f is a scalar and x is an n-vector whose components are unconstrained. We consider the comparative evaluation of algorithms for unconstrained minimization. We are concerned with the measurement of the computational speed and examine critically the concept of equivalent number of function evaluations Ne, which is defined by
Here, N0 is the number of function evaluations; N1 is the number of gradient evaluations; N2 is the number of Hessian evaluations? n is the dimension of the vector x; and m = n(n+l)/2 is the number of elements of the Hessian matrix above and including the principal diagonal. We ask the following question: Does the use of the quantity Ne constitute a fair way of comparing different algorithms?
This study was supported by the National Science Foundation, Grant No. ENG-79-18667.
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References
Miele, A., Gonzalez, S., and Wu, A.K., On Testing Algorithms for Mathematical Programming Problems, Rice University, Aero-Astronautics Report No. 134, 1976.
Miele, A., and Gonzalers. S., On the Comparative Evaluation of Algorithms for Mathematical Programming Problems, Nonlinear Programming 3, Edited by O.L. Mangasarian, R.R. Meyer, and S.M. Robinson, Academic Press, New York, New York, pp. 337–359, 1978.
Gonzalez, S., Comparison of Mathematical Programming Algorithms, Based on the CPU Time (in Spanish), UNAM, Institute of Engineering, Mexico City, Mexico, Report No. 8196, 1979.
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© 1982 Springer-Verlag Berlin Heidelberg
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Miele, A. (1982). Remarks on the Comparative Evaluation of Algorithms for Mathematical Programming Problems. In: Mulvey, J.M. (eds) Evaluating Mathematical Programming Techniques. Lecture Notes in Economics and Mathematical Systems, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95406-1_36
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DOI: https://doi.org/10.1007/978-3-642-95406-1_36
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