## Goldstein-Price Function

### Description:

*Dimensions: 2*

The Goldstein-Price function has several local minima.

### Input Domain:

The function is usually evaluated on the square x_{i}∈ [-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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