  We consider centralized and distributed mirror descent algorithms over a
finite-dimensional Hilbert space, and prove that the problem variables converge
to an optimizer of a possibly nonsmooth function when the step sizes are square
summable but not summable. Prior literature has focused on the convergence of
the function value to its optimum. However, applications from distributed
optimization and learning in games require the convergence of the variables to
an optimizer, which is generally not guaranteed without assuming strong
convexity of the objective function. We provide numerical simulations comparing
entropic mirror descent and standard subgradient methods for the robust
regression problem.
