Distributed Abstract Optimization via Constraints Consensus: Theory and Applications

Distributed abstract programs are a novel class of distributed optimization problems where i) the number of variables is much smaller than the number of constraints and ii) each constraint is associated to a network node. Abstract optimization programs are a generalization of linear programs that captures numerous geometric optimization problems. We propose novel constraints consensus algorithms for distributed abstract programs with guaranteed finite-time convergence to a global optimum. The algorithms rely upon solving local abstract programs and exchanging the solutions among neighboring processors. The proposed algorithms are appropriate for networks with weak time-dependent connectivity requirements and tight memory constraints. We show how the constraints consensus algorithms may be applied to suitable target localization and formation control problems.