Solution of the Least Squares Method problem of pairwise comparison matrices


Autoria(s): Bozóki, Sándor
Data(s)

2008

Resumo

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.

Formato

application/pdf

Identificador

http://unipub.lib.uni-corvinus.hu/748/1/Bozoki2008_manu.pdf

Bozóki, Sándor (2008) Solution of the Least Squares Method problem of pairwise comparison matrices. Central European Journal of Operations Research, 16 (4). pp. 345-358. DOI 10.1007/s10100-008-0063-1 <http://dx.doi.org/10.1007/s10100-008-0063-1>

Publicador

Springer

Relação

http://unipub.lib.uni-corvinus.hu/748/

http://www.springerlink.com/content/b2257h112256v32n/

10.1007/s10100-008-0063-1

Palavras-Chave #Mathematics, Econometrics
Tipo

Article

PeerReviewed

Idioma(s)

en

en