BOBYQA performs derivative-free bound-constrained optimization using an iteratively constructed quadratic approximation for the objective function.

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`x0` |
starting point for searching the optimum. |

`fn` |
objective function that is to be minimized. |

`lower, upper` |
lower and upper bound constraints. |

`nl.info` |
logical; shall the original NLopt info been shown. |

`control` |
list of options, see |

`...` |
additional arguments passed to the function. |

This is an algorithm derived from the BOBYQA Fortran subroutine of Powell, converted to C and modified for the NLOPT stopping criteria.

List with components:

`par` |
the optimal solution found so far. |

`value` |
the function value corresponding to |

`iter` |
number of (outer) iterations, see |

`convergence` |
integer code indicating successful completion (> 0) or a possible error number (< 0). |

`message` |
character string produced by NLopt and giving additional information. |

Because BOBYQA constructs a quadratic approximation of the objective, it may perform poorly for objective functions that are not twice-differentiable.

M. J. D. Powell. “The BOBYQA algorithm for bound constrained optimization without derivatives,” Department of Applied Mathematics and Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009).

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