Paper Info
Title
Solution of the least squares method problem of pairwise comparison matrices.
Abstract
The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.
Year
DOI
Venue
2008
10.1007/s10100-008-0063-1
CEJOR
Keywords
Field
DocType
Pairwise comparison matrix,Least squares approximation,Polynomial system,Homotopy method,Incomplete pairwise comparison matrix
Least squares,Pairwise comparison,Mathematical optimization,Nonlinear system,Global optimization,Matrix (mathematics),System of polynomial equations,Maxima and minima,Optimization problem,Mathematics
Journal
Volume
Issue
ISSN
16
4
1435-246X
Citations 
PageRank 
References 
13
1.45
5
Authors
1
Name
Order
Citations
PageRank
Sándor Bozóki115810.98