A new zero-order 1-D optimization algorithm: trichotomy method
For researchers and practitioners needing efficient 1D optimization, this method offers a modest improvement over existing techniques.
The paper proposes a new 1D optimization algorithm, the trichotomy method, which reduces the interval of uncertainty by a factor of three each iteration. It requires fewer function evaluations and achieves better accuracy compared to interval halving, golden section, and Fibonacci search methods.
A new 1D search method is proposed for minimizing an arbitrary real valued function. The algorithm is a modification of the interval halving method which is based on dividing the interval of uncertainty by three points into four equal parts. The trichotomy method is based on dividing the interval by five points into six equal parts and provides the interval reducing exactly three times in every iteration. New algorithm's performance has been extensively tested and compared to well-known 1D search algorithms: the interval halving method, golden section method, Fibonacci search. The results show that the trichotomy method usually require less calculations of the values of the minimized function to determine the minimum point with the given accuracy. Also it has better accuracy when finding the minimum point after using N calculations of the function values.