A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization

Understand

Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration.

• The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by V\~u and Condat that includes the well known ADMM as a particular case.
• The obtained algorithm is used to solve asynchronously a distributed optimization problem.
• A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective.