## Abstract

We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step.

Original language | English |
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Article number | 3043 |

Journal | Mathematics |

Volume | 9 |

Issue number | 23 |

DOIs | |

Publication status | Published - 1 Dec 2021 |

## Keywords

- Global optimisation
- Parallelisation of algorithms
- Pure random search
- Rate of convergence
- Stochastic algorithms