On a Global Optimization Problem in the Study of Information Discrepancy

A nonlinear function has been introduced for indexing the disagreement degree of a group of judgment matrices (in FW, 1994). It has many good properties and may be applied in decision making and information process. In this paper, we will discuss a global optimization problem concerned with the global maximum of this function which is constrained on some sets of matrices. Because the size of matrix groups in the problem is arbitrary and the number of local maximum solutions increases exponentially, numerical methods are not suitable and formalized results are desired for the problem. By an approach somewhat similar to the branch and bounded method, we have obtained some formulae on global maximums, a su cient and necessary condition of the function's taking the maximums, and its some maximum solution sets.