Visualization of hypersurfaces and multivariable (objective) functions by partial global optimization

Hypersurfaces of the type z=F(x1,...,xn), where F are single-valued functions of n real variables, cannot be visualized directly due to our inability to perceive dimensions higher than three. However, by projecting them down to two or three dimensions many of their properties can be revealed. In this paper a method to generate such projections is proposed, requiring successive global minimizations and maximizations of the function with respect to n-1 or n-2 variables. A number of examples are given to show the usefulness of the method, particularly for optimization problems where there is a direct interest in the minimum or maximum domains of objective functions.