Bozóki, Sándor (2008) Solution of the least squares method problem of pairwise comparison matrices. CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH, 16 (4). pp. 345358. ISSN 1435246X

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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 nonconvex 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 

Subjects:  H Social Sciences / társadalomtudományok > HB Economic Theory / közgazdaságtudomány H Social Sciences / társadalomtudományok > HB Economic Theory / közgazdaságtudomány > HB5 Mathematical economics / matematikai közgazdaságtan Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra 
Depositing User:  Dr. Sándor Bozóki 
Date Deposited:  11 Sep 2018 13:09 
Last Modified:  11 Sep 2018 13:09 
URI:  http://real.mtak.hu/id/eprint/83508 
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