For questions related to deterministic annealing (DA), the method used for the solution of several nonconvex problems offers the ability to avoid shallow local minima of a given cost surface and the ability to minimize the cost function even when there are many local minima
Deterministic annealing is used in order to avoid local minima of the given cost function which traps traditional techniques. A set of temperature parametrized Gibbs probability density functions relate each data point to each cluster.
The method is established in a probabilistic framework through basic information-theoretic techniques such as maximum entropy and random coding. It arises naturally in the context of statistical mechanics by the emulation of a physical process whereby a solid is slowly cooled and at zero temperature assumes its minimum energy configuration