Global optimization: the Alienor mixed method with Piyavskii‐Shubert technique

Abstract

Purpose

Aims to present study of the coupling of the Alienor method with the algorithm of Piyavskii‐Shubert for global optimization applications.

Design/methodology/approach

The Alienor method allows us to transform a multivariable function into a function of a single variable for which it is possible to use an efficient and rapid method for calculating the global optimum. This simplification is based on the use of the established Alienor methodology.

Findings

The Alienor method allows us to transform a multidimensional problem into a one‐dimensional problem of the same type. It was then possible to use the Piyavskii‐Shubert method based on sub‐estimators of the objectives function. The obtained algorithm from coupling the two methods was found to be simple and easy to implement on any multivariable function.

Research limitations/implications

This method does not require derivatives and the convergence of the algorithm is relatively rapid if the Lipschitz constant is small.

Practical implications

The classical multidimensional global optimization methods involve great difficulties for their implementation to high dimensions. The coupling of two established methods produces a practical easy to implement technique.

Originality/value

New method couples two established ones and produces a simple and user‐friendly technique.

Citation

Ziadi, A., Guettal, D. and Cherruault, Y. (2005), "Global optimization: the Alienor mixed method with Piyavskii‐Shubert technique", Kybernetes, Vol. 34 No. 7/8, pp. 1049-1058. https://doi.org/10.1108/03684920510605867