11 | | It does ''not'' assume that {{{f(x)}}} is known in analytical form: {{{f(x)}}} is simply a black-box that, given input values, produces output values. The bounds on the variables {{{x_L, x_U}}} are assumed to be finite. '''RBFOpt''' is especially targeted at problems for which each evaluation of the objective function {{{f(x)}}} is expensive (in terms of computing time, or cost, or some other measure) and we want to find a ''global'' minimum of the function with as few function evaluations as possible. Since this is a very difficult class of problems (we do not assume availability of first order derivatives), '''RBFOpt''' works best on problems that are relatively small dimensional (up to 20 variables, ideally less than 10) and for which the bounding box is not too large. |
| 11 | It does ''not'' assume that {{{f(x)}}} is known in analytical form: {{{f(x)}}} is simply a black-box that, given input values, produces output values. The bounds on the variables {{{x_L, x_U}}} are assumed to be finite. '''RBFOpt''' is especially targeted at problems for which each evaluation of the objective function {{{f(x)}}} is expensive (in terms of computing time, or cost, or some other measure) and we want to find a ''global'' minimum of the function with as few function evaluations as possible. Since this is a very difficult class of problems (we do not assume availability of first order derivatives), '''RBFOpt''' works best on problems that are relatively small dimensional (a 10-40 variables) and for which the bounding box is not too large. However, it has been successfully employed on problems on much larger sizes. |