Powell direction set method Powell's gradient-free methods[20] provide directions of search that line up with directions conjugate about the Hessian matrix of the quadratic approximation to the objective function. The Powell method applied in the current study is the version described in[21, 1], in which an initial guess and a set of independent search directions are provided to the algorithm. In each iteration the method serially performs a sequence of line minimizations along the various directions in the space of parameters. At the end of each iteration the method replaces one of the original directions with the line joining the starting and ending points. The Figure 3 illustrates the Powell method. Care is taken to ensure that the di-