Distributed optimization via adaptive regularization for large problems with separable constraints

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 convergence 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.