On a Global Optimization Problem in the Study of Information Discrepancy

A nonlinear function has been introduced for indexing the disagreementdegree of a group of judgment matrices (Weiwu Fang, 1994). It has many goodproperties and may be applied in decision making and information processes.In this paper, we will discuss a global optimization problem concerned withthe global maximum of this function which is constrained on some sets ofmatrices. Because the size of matrix groups in the problem is arbitrary andthe number of local maximum solutions increases exponentially, numericalmethods are not suitable and formalized results are desired for the problem.By an approach somewhat similar to the branch and bound method, we haveobtained some formulae on global maximums, a sufficient and necessarycondition of the function taking the maximums, and some maximum solutionsets.