Vianney Bruned, André Mas, Sylvain Wlodarczyk
Published 2018-11-10Version 1
Particle swarm optimization algorithm is a stochastic meta-heuristic solving global optimization problems appreciated for its efficacity and simplicity. It consists in a swarm of particles interacting among themselves and searching the global optimum. The trajectory of the particles has been well-studied in a deterministic case and more recently in a stochastic context. Assuming the convergence of PSO, we proposed here two CLT for the particles corresponding to two kinds of convergence behavior. These results can lead to build confidence intervals around the local minimum found by the swarm or to the evaluation of the risk. A simulation study confirms these properties.
Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs
Weak Convergence (IIA) - Functional and Random Aspects of the Univariate Extreme Value Theory
On the paper ``Weak convergence of some classes of martingales with jumps''
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