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.
Keywords
Citation
Mora, G., Cherruault, Y. and Ubeda, J.I. (2005), "Solving inequalities by
Publisher
:Emerald Group Publishing Limited
Copyright © 2005, Emerald Group Publishing Limited