DIMACS TR: 97-04
On a Global Optimization Problem in the Study of Information Discrepancy
Author: Weiwu FANG
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 sufficient and necessary
condition of the function's taking the maximums, and its some
maximum solution sets.
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