An algorithm for minimization of arbitrary generic functions in one dimension over a finite domain

TL;DR

This paper introduces a new one-dimensional minimization algorithm that effectively handles irregular functions with multiple local minima over finite domains, improving upon existing methods like Brent's in convergence speed and robustness.

Contribution

The proposed algorithm advances one-dimensional minimization by managing multiple local minima and finite domain constraints, with better convergence than Brent's method.

Findings

Outperforms Brent's method in convergence speed.

Effectively handles highly irregular functions with multiple minima.

Suitable for finite domain minimization problems.

Abstract

A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be applied in "difficult" cases, that is when the function is highly irregular and has multiple sub-optimal local minima. The algorithm uses quadratic or cubic interpolation and subdivision of intervals in golden ratio as a last resort. It improves over Brent's method and similar ones in several aspects. It manages multiple local minima, takes into account the complications of having to deal with a finite domain, rather than an unlimited one, and has a slightly faster convergence in most cases.