  Quadratic programs arise in robotics, communications, smart grids, and many
other applications. As these problems grow in size, finding solutions becomes
more computationally demanding, and new algorithms are needed to efficiently
solve them at massive scales. Targeting large-scale problems, we develop a
multi-agent quadratic programming framework in which each agent updates only a
small number of the total decision variables in a problem. Agents communicate
their updated values to each other, though we do not impose any restrictions on
the timing with which they do so, nor on the delays in these transmissions.
Furthermore, we allow weak parametric coupling among agents, in the sense that
they are free to independently choose their step sizes, subject to mild
restrictions. We further provide the means for agents to independently
regularize the problems they solve, thereby improving convergence properties
while preserving agents' independence in selecting parameters and ensuring a
global bound on regularization error is satisfied. Larger regularizations
accelerate convergence but increase error in the solution obtained, and we
quantify the trade off between convergence rates and quality of solutions.
Simulation results are presented to illustrate these developments.
