On some convexity properties of the Least Squares Method for pairwise comparisons matrices without the reciprocity condition

被引：7
作者：
Fueloep, J. [1 ]
Koczkodaj, W. W. [2 ]
Szarek, S. J. [3 ,4 ]
机构：
[1] Hungarian Acad Sci, Res Grp Operat Res & Decis Syst, Comp & Automat Res Inst, H-1518 Budapest, Hungary
[2] Laurentian Univ, Sudbury, ON P3E 2C6, Canada
[3] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA
[4] Univ Paris 06, F-75252 Paris, France
来源：
JOURNAL OF GLOBAL OPTIMIZATION | 2012年 / 54卷 / 04期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Pairwise comparisons; Convexity properties; SCALING METHOD; HIERARCHICAL STRUCTURES; DERIVING WEIGHTS; PRIORITIES; APPROXIMATION;
D O I：
10.1007/s10898-011-9785-z
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The relaxation of the reciprocity condition for pairwise comparisons is revisited from the optimization point of view. We show that some special but not extreme cases of the Least Squares Method are easy to solve as convex optimization problems after suitable nonlinear change of variables. We also give some other, less restrictive conditions under which the convexity of a modified problem can be assured, and the global optimal solution of the original problem found by using local search methods. Mathematical and psychological justifications for the relaxation of the reciprocity condition as well as numerical examples are provided.
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页码：689 / 706
页数：18
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