Totally Asynchronous Large-Scale Quadratic Programming: Regularization, Convergence Rates, and Parameter Selection

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 multiagent 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 agents to independently choose their stepsizes, 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. Larger regularizations accelerate convergence but increase the error in the solution obtained, and we quantify the tradeoff between convergence rates and quality of solutions. Simulation results are presented to illustrate these developments.