Algebraic Stability Analysis of Particle Swarm Optimization Using Stochastic Lyapunov Functions and Quantifier Elimination

This paper adds to the discussion about theoretical aspects of particle swarm stability by proposing to employ stochastic Lyapunov functions and to determine the convergence set by quantifier elimination. We present a computational procedure and show that this approach leads to a reevaluation and extension of previously known stability regions for PSO using a Lyapunov approach under stagnation assumptions.