Description Usage Arguments Details Value Note References See Also Examples

Find minimum of single-variable function on fixed interval.

1 2 |

`f` |
function whose minimum or maximum is to be found. |

`a, b` |
endpoints of the interval to be searched. |

`maxiter` |
maximal number of iterations. |

`maximum` |
logical; shall maximum or minimum be found; default FALSE. |

`tol` |
relative tolerance; left over for compatibility. |

`rel.tol, abs.tol` |
relative and absolute tolerance. |

`...` |
additional variables to be passed to the function. |

fminbnd finds the minimum of a function of one variable within a fixed interval. It applies Brent's algorithm, based on golden section search and parabolic interpolation.

`fminbnd`

may only give local solutions.
`fminbnd`

never evaluates `f`

at the endpoints.

List with

`xmin` |
location of the minimum resp. maximum. |

`fmin` |
function value at the optimum. |

`niter` |
number of iterations used. |

`estim.prec` |
estimated precision. |

`fminbnd`

mimics the Matlab function of the same name.

R. P. Brent (1973). Algorithms for Minimization Without Derivatives. Dover Publications, reprinted 2002.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## CHEBFUN example by Trefethen
f <- function(x) exp(x)*sin(3*x)*tanh(5*cos(30*x))
fminbnd(f, -1, 1) # fourth local minimum (from left)
g <- function(x) complexstep(f, x) # complex-step derivative
xs <- findzeros(g, -1, 1) # local minima and maxima
ys <- f(xs); n0 <- which.min(ys) # index of global minimum
fminbnd(f, xs[n0-1], xs[n0+1]) # xmin:0.7036632, fmin: -1.727377
## Not run:
ezplot(f, -1, 1, n = 1000, col = "darkblue", lwd = 2)
ezplot(function(x) g(x)/150, -1, 1, n = 1000, col = "darkred", add = TRUE)
grid()
## End(Not run)
``` |

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