  We take a new perspective on the weighted sum-rate maximization in
multiple-input multiple-output (MIMO) interference networks, by formulating an
equivalent max-min problem. This seemingly trivial reformulation has
significant implications: the Lagrangian duality of the equivalent max-min
problem provides an elegant way to establish the sum-rate duality between an
interference network and its reciprocal when such a duality exists, and more
importantly, suggests a novel iterative minimax algorithm for the weighted
sum-rate maximization. Moreover, the design and convergence proof of the
algorithm use only general convex analysis. They apply and extend to any
max-min problems with similar structure, and thus provide a general class of
algorithms for such optimization problems. This paper presents a promising step
and lends hope for establishing a general framework based on the minimax
Lagrangian duality for characterizing the weighted sum-rate and developing
efficient algorithms for general MIMO interference networks.
