  Consider the setting where each vertex of a graph has a function, and
communications can only occur between vertices connected by an edge. We wish to
minimize the sum of these functions. For the case when each function is the sum
of a strongly convex quadratic and a convex function, we propose a distributed
version of Dykstra's algorithm. The computations to optimize the dual objective
function can run asynchronously without a global clock, and in a distributed
manner without a central controller. Convergence to the primal minimizer is
deterministic instead of being probabilistic, and is guaranteed as long as in
each cycle, the edges where two-way communications occur connects all vertices.
We also look at an accelerated algorithm, and an algorithm for the case when
the functions on the nodes are not strongly convex.
