Entropy minimization, \(DAD\) problems, and doubly stochastic kernels (Q1332191)

The classical \(DAD\) problem asks, for a square matrix \(A\) with nonnegative entries, when it is possible to find positive diagonal matrices \(D_ 1\) and \(D_ 2\) with \(D_ 1 AD_ 2\) doubly stochastic. The authors consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques the authors obtain strong analogues of the classical results. The techniques leading to the main results comprise a mixture of variational and fixed point methods. Many of the results appear inaccessible without the combined use of both approaches.