  Many practical applications require solving an optimization over large and
high-dimensional data sets, which makes these problems hard to solve and
prohibitively time consuming. In this paper, we propose a parallel distributed
algorithm that uses an adaptive regularizer (PDAR) to solve a joint
optimization problem with separable constraints. The regularizer is adaptive
and depends on the step size between iterations and the iteration number. We
show theoretical converge of our algorithm to an optimal solution, and use a
multi-agent three-bin resource allocation example to illustrate the
effectiveness of the proposed algorithm. Numerical simulations show that our
algorithm converges to the same optimal solution as other distributed methods,
with significantly reduced computational time.
