Solution of the least squares method problem of pairwise comparison matrices

Sándor Bozóki ()

Central European Journal of Operations Research, 2008, vol. 16, issue 4, 345-358

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. Copyright Springer-Verlag 2008

Keywords: Pairwise comparison matrix; Least squares approximation; Polynomial system; Homotopy method; Incomplete pairwise comparison matrix (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10100-008-0063-1

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