We consider the Noisy MIMO Interference Channel (IFC) with linear 
transmitters and receivers and full CSI. The maximization of the 
Weighted Sum Rate (WSR) or transceiver design for Interference Alignment (IA)
lead to cost functions with many local optima. Deterministic annealing is an approach 
that allows to track the variation of the known solution of one version of the problem
into the unknown solution of the desired version by a controlled variation of a parameter
called temperature. When the temperature parameter is chosen as inverse SNR (or noise power),
the transceiver design for maximum WSR is known at low SNR and can be tracked to any desired
SNR, yielding an elegant technique to find the global optimum. The solution includes filter
design for the progressive switching on of streams as the SNR increases.
For IA on the other hand, IA feasibility is unchanged when the MIMO crosslink channel 
matrices have a reduced rank equal to the maximum of the number of streams passing through
them in forward and dual IFC (this would correspond to LOS channels in the case of single
streams). The rank reduction simplifies IA design and feasibility analysis, and allows
in particular a counting of the number of IA solutions. By choosing now the temperature
parameter to be a scale factor for the remaining channel singular values, the solution for
reduced rank channels can be evolved into that for arbitrary channels.