Global convergence analysis of swarm optimization using paracontraction and semistability theory
Qing Hui, Haopeng Zhang · 2016
We prove the global convergence of the original, standard version of particle swarm optimization (PSO) under some mild, matricial and algebraic, practically checkable conditions. Our method is based on a novel integration of miscellaneous techniques from matrix paracontraction in numerical analysis and semistability in control theory. The proposed analysis framework is quite general and can be used to analyze global convergence of many variants of PSO and other types of swarm optimization algorithms such as multiagent coordination optimization (MCO).