Efficient Partition of N-Dimensional Intervals in the Framework of One-Point-Based Algorithms

In this paper, the problem of the minimal description of the structure of a vector function f(x) over an $N$-dimensional interval is studied. Methods adaptively subdividing the original interval in smaller subintervals and evaluating f(x) at only one point within each subinterval are considered. Two partition strategies traditionally used for solving this problem are analyzed. A new partition strategy based on an efficient technique developed for diagonal algorithms is proposed and studied.