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Solution of the Least Squares Method problem of pairwise comparison matrices

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

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


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.

Item Type:Article
Uncontrolled Keywords:pairwise comparison matrix, least squares approximation, polynomial system, homotopy method, incomplete pairwise comparison matrix
Subjects:Mathematics, Econometrics
Projects:OTKA K 60480
DOI:10.1007/s10100-008-0063-1
ID Code:748
Deposited By: Ádám Hoffmann
Deposited On:04 Jul 2012 14:33
Last Modified:05 Sep 2012 07:50

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