STK_TESTFUN_HARTMAN6 computes the "Hartman6" function
The Hartman6 function is a test function in dimension 6, which is
part of the famous Dixon & Szego benchmark [1] in global optimization.
It is usually minimized over [0, 1]^6.
HISTORICAL REMARKS
This function belongs to a general class of test functions
introduced by Hartman [2], hence the name.
The particular set of coefficients used in the definition of the
"Hartman6" function, however, seems to have been introduced by [1].
GLOBAL MINIMUM
According to [4], the function has one global minimum at
x = [0.20169 0.150011 0.476874 0.275332 0.311652 0.657300].
The corresponding function value is:
f(x) = -3.322368011391339
A slightly lower value is attained [5] at
x = [0.20168952 0.15001069 0.47687398 ...
0.27533243 0.31165162 0.65730054]
The corresponding function value is:
f(x) = -3.322368011415512
The exact global optimum does not appear to be known.
REFERENCES
[1] L. C. W. Dixon & G. P. Szego (1978). Towards Global
Optimization 2, North-Holland, Amsterdam, The Netherlands
[2] J. K. Hartman (1973). Some experiments in global optimization.
Naval Research Logistics Quarterly, 20(3):569-576.
[3] V. Picheny, T. Wagner & D. Ginsbourger (2013). A benchmark
of kriging-based infill criteria for noisy optimization.
Structural and Multidisciplinary Optimization, 48:607-626.
[4] S. Surjanovic & D. Bingham. Virtual Library of Simulation
Experiments: Test Functions and Datasets. Retrieved March 3,
2022, https://www.sfu.ca/~ssurjano/hart4.html.
[5] O. Roustant, D. Ginsbourger & Y. Deville (2012).
DiceKriging package, version 1.6.0 from 2021-02-23
URL: https://cran.r-project.org/web/packages/DiceKriging/index.html