Consensus based optimization: Difference between revisions

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</math> determines the communication radius of particles. This choice corresponds to a local convex regularization of the objective function <math>f

</math>.

* [[Mean-shift algorithm|'''Mean-shift algorithm''']]<ref>{{Cite journal |last=Fukunaga |first=K. |last2=Hostetler |first2=L. |date=January 1975-01 |title=The estimation of the gradient of a density function, with applications in pattern recognition |url=http://ieeexplore.ieee.org/document/1055330/ |journal=IEEE Transactions on Information Theory |language=en |volume=21 |issue=1 |pages=32–40 |doi=10.1109/TIT.1975.1055330 |issn=0018-9448}}</ref>: Employing polarized CBO for a constant objective function <math>f

</math>, together with no noise (i.e. <math>\sigma = 0

</math>) and an Euler–Maruyama discretization with step size <math>dt=1

</math>, corresponds to the mean-shift algorithm.

* '''Bounded confidence model''': When choosing a constant objective function, no noise model, but also the special kernel function <math>k(x,\tilde x) = 1_{\|x-\tilde x\| \leq \kappa}

</math>, the SDE in {{EquationNote|2=(1)}} transforms to a ODE known as the bounded confidence model<ref>{{Cite journal |last=Deffuant |first=Guillaume |last2=Neau |first2=David |last3=Amblard |first3=Frederic |last4=Weisbuch |first4=Gérard |date=January 2000-01 |title=Mixing beliefs among interacting agents |url=https://www.worldscientific.com/doi/abs/10.1142/S0219525900000078 |journal=Advances in Complex Systems |language=en |volume=03 |issue=01n04 |pages=87–98 |doi=10.1142/S0219525900000078 |issn=0219-5259}}</ref>, which arises in opinion dynamics.

== See also ==