ON A CLASS OF GLOBAL OPTIMIZATION TEST FUNCTIONS
This paper provides a theoretical proof illustrating that for a certain class of functions having the property that the partial derivatives have the same equation with respect to all variables, the optimum value (minimum or maximum) takes place at a point where all the variables have the same value. This information will help the researchers working with high dimensional functions to minimize the computational burden due to the fact that the search has to be performed only with respect to one variable.
global optimization multidimensional functions first partial derivatives