Solving inequalities by α‐dense curves. Application to global optimization

Abstract

Purpose

To introduce an algorithm to solve inequalities defined by real functions on a certain compact set D of a general metric space (E, D). The device is based on α‐dense curves.

Design/methodology/approach

The solution of inequalities using α‐dense curves and also an approach to a global optimization technique, similarly obtained to that of the inequalities.

Findings

A new method is presented. The algorithm for solving inequalities is described which is based on a proven result. Inequalities of n‐variable dependence are reduced by transformation using α‐dense curves.

Research limitations/implications

The research is a continuation of studies that resulted in a new method called Alienor for solving global optimization problems associated with multi‐variable functions.

Originality/value

Based on earlier research by the authors α‐dense curves have been used which allow the transformation of a n‐variables global optimization problem into a one‐variable global one. This paper gives a new method for quickly solving the one‐variable problem.

Citation

Mora, G., Cherruault, Y. and Ubeda, J.I. (2005), "Solving inequalities by α‐dense curves. Application to global optimization", Kybernetes, Vol. 34 No. 7/8, pp. 983-991. https://doi.org/10.1108/03684920510605803