Virtual Library of Simulation Experiments:

Test Functions and Datasets

Goldstein-Price Function


Description:

Dimensions: 2

The Goldstein-Price function has several local minima.

Input Domain:

The function is usually evaluated on the square xi ∈ [-2, 2], for all i = 1, 2.

Global Minimum:



Modifications and Alternate Forms:

Picheny et al. (2012) use the following logarithmic form of the Goldstein-Price function, on [0, 1]2:

This rescaled form of the function has a mean of zero and a variance of one. The authors also add a small Gaussian error term to the output.

Code:


References:

Dixon, L. C. W., & Szego, G. P. (1978). The global optimization problem: an introduction. Towards global optimization, 2, 1-15.

Molga, M., & Smutnicki, C. Test functions for optimization needs (2005). Retrieved June 2013, from http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf.

Picheny, V., Wagner, T., & Ginsbourger, D. (2012). A benchmark of kriging-based infill criteria for noisy optimization.


For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.



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