STK_TESTFUN_HARTMAN4 computes the "Hartman4" function

 CALL: Y = stk_testfun_hartman4 (X)

    computes the value Y of the Hartman4 function at X.

    The Hartman4 function is a test function in dimension 4,
    which is usually minimized over [0, 1]^4. 

 HISTORICAL REMARKS

    This function belongs to a general class of test functions introduced
    by Hartman [1].  The particular set of coefficients used in the
    Hartman4 function seems to have been introduced by [2].

    Note that the test function used in [2] is a scaled version of the
    one implemented here, which can be recovered as follows:

      y = (1.1 + stk_testfun_hartman4 (x)) / 0.839;

    Picheny & co-authors [2] refer to Dixon & Szego [3] for this test
    function, but it turns out that [3] only contains two sorts of
    "Hartman functions", in dimensions three and six.

    In fact, this function appears to have been obtained by truncating
    the sum at the fourth coordinate in the six-dimensional Hartman
    function of [3].

 GLOBAL MINIMUM

    According to [4], the function has one global minimum at

       x = [0.1873 0.1906 0.5566 0.2647].

    The corresponding function value, with our definition of the test
    function, is:

       f(x) = -3.729722308557300.

    Slightly better function values can be found in the neighborhood of
    this point.  For instance, with

       x = [0.18744768 0.19414868 0.558005333 0.26476409]

    we get

       f(x) = -3.729840440436292.

 REFERENCES

  [1] J. K. Hartman (1973).  Some experiments in global optimization.
      Naval Research Logistics Quarterly, 20(3):569-576.

  [2] V. Picheny, T. Wagner & D. Ginsbourger (2013).  A benchmark
      of kriging-based infill criteria for noisy optimization.
      Structural and Multidisciplinary Optimization, 48:607-626.

  [3] L. C. W. Dixon & G. P. Szego (1978).  Towards Global
      Optimization 2, North-Holland, Amsterdam, The Netherlands

  [4] V. Picheny, D. Ginsbourger & O. Roustant (2021).  DiceOptim:
      Kriging-Based Optimization for Computer Experiments.  R package
      version 2.1.1.  URL: https://CRAN.R-project.org/package=DiceOptim.