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