# Available Algorithms¶

There are currently 13 optimization algorithms implemented in `MXMCPy`

. The algorithms are listed below along with some general information.

## Multi-level Monte Carlo¶

Algorithm Name | Optimization | Sampling Strategy |
---|---|---|

MLMC | Analytic | Recursive Difference |

Ref: Giles, M. B.: Multi-level Monte Carlo path simulation. Operations Research , vol. 56, no. 3, 2008, pp. 607–617.

## Multifidelity Monte Carlo¶

Algorithm Name | Optimization | Sampling Strategy |
---|---|---|

MFMC | Analytic | Multifidelity |

Ref: Peherstorfer, B.; Willcox, K.; and Gunzburger, M.: Optimal Model Management for Multifidelity Monte Carlo Estimation. SIAM Journal on Scientific Computing, vol. 38, 01 2016, pp. A3163–A3194

## Approximate Control Variates¶

Algorithm Name | Optimization | Sampling Strategy |
---|---|---|

WRDIFF | Numerical | Recursive Difference |

ACVIS | Numerical | Independent Samples |

ACVMF | Numerical | Multifidelity |

ACVKL | Numerical | Multifidelity |

Ref: Gorodetsky, A.; Geraci, G.; Eldred, M.; and Jakeman, J. D.: A generalized approximate control variate framework for multifidelity uncertainty quantification. Journal of Computational Physics, 2020, p. 109257

## Parametrically-defined Approximate Control Variates¶

Algorithm Name | Optimization | Sampling Strategy |
---|---|---|

GRDSR | Numerical | Recursive Difference |

GRDMR | Numerical | Recursive Difference |

GISSR | Numerical | Independent Samples |

GISMR | Numerical | Independent Samples |

ACVMFU | Numerical | Multifidelity |

GMFSR | Numerical | Multifidelity |

GMFMR | Numerical | Multifidelity |

Ref: Bomarito, G. F., Leser, P. E., Warner, J. E., and Leser, W. P: On the Optimization of Approximate Control Variates with Parametrically-Defined Estimators. In Preparation.