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

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