Paracontracting Multiagent Coordination Optimization: Convergence and parallelization

In this paper, a contraction mapping based Multiagent Coordination Optimization (MCO) algorithm, called Paracontracting Multiagent Coordination Optimization (PMCO), is proposed and implemented in a parallel computing way by embedding MATLAB built-in function parfor into PMCO. Then we give a global convergence result of PMCO by means of paracontraction and semistability theory. The basic idea here is to convert the proposed derivative-free iterative algorithm for PMCO into a discrete-time switched linear system and then discuss its semistability property. Based on some matrix analysis results and semistability theory, we present two sufficient conditions for guaranteeing the global convergence of PMCO under different circumstances. Finally, numerical evaluation of the parallel PMCO algorithm is provided in the paper by running the proposed algorithm on multicore supercomputers.