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

TL;DR

This paper investigates efficient methods for partitioning N-dimensional intervals in one-point-based algorithms, introducing a new strategy that improves upon traditional approaches by leveraging techniques from diagonal algorithms.

Contribution

It proposes a novel partition strategy for N-dimensional intervals that enhances the efficiency of one-point-based algorithms, supported by analysis and comparison with existing methods.

Findings

The new partition strategy outperforms traditional methods in certain scenarios.

Analysis shows improved convergence properties with the proposed technique.

The approach reduces the number of function evaluations needed.

Abstract

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.