Multidimensional global optimization using interval slopes
The knowledge of a good enclosure of the range of a function over small interval regions allows us to avoid convergence of optimization algorithms to a non-global point(s). We used interval slopes f [X, x] to check for monotonicity and integrated their derivative forms g[X, x], x is an element of X by quadratic and Newton methods to obtain narrow enclosures. In order to include boundary points in the search for the optimum point(s), we expanded the initial box by a small width on each dimension. These procedures resulted in an improvement in the algorithm proposed by Hansen [4].
interval slopes monotonicity newton method convexity quadratic method