Local tuning and partition strategies for diagonal GO methods

TL;DR

This paper introduces diagonal geometric methods with local tuning and partition strategies for global optimization of multiextremal functions, demonstrating significant acceleration over traditional methods through numerical comparisons.

Contribution

It extends a one-dimensional local tuning approach to multi-dimensional problems using diagonal partition strategies, establishing convergence and improving efficiency.

Findings

Methods achieve faster convergence than traditional approaches.

Local Lipschitz constant estimates enhance optimization speed.

Numerical results confirm strong acceleration in diverse test cases.

Abstract

In this paper, global optimization (GO) Lipschitz problems are considered where the multi-dimensional multiextremal objective function is determined over a hyperinterval. An efficient one-dimensional GO method using local tuning on the behavior of the objective function is generalized to the multi-dimensional case by the diagonal approach using two partition strategies. Global convergence conditions are established for the obtained diagonal geometric methods. Results of a wide numerical comparison show a strong acceleration reached by the new methods working with estimates of the local Lipschitz constants over different subregions of the search domain in comparison with the traditional approach.