  This note considers the problem of minimizing interacting free energy.
Motivated by the mirror descent algorithm, for a given interacting free energy,
we propose a descent dynamics with a novel metric that takes into consideration
the reference measure and the interacting term. This metric naturally suggests
a monotone reparameterization of the probability measure. By discretizing the
reparameterized descent dynamics with the explicit Euler method, we arrive at a
new mirror-descent-type algorithm for minimizing interacting free energy.
Numerical results are included to demonstrate the efficiency of the proposed
algorithms.
