# scipy.optimize.minimize_scalar

scipy.optimize.minimize_scalar(fun, bracket=None, bounds=None, args=(), method='brent', tol=None, options=None)

  Minimization of scalar function of one variable.

  Parameters
    fun callable

      Objective function. Scalar function, must return a scalar.

    bracket sequence, optional

      For methods ‘brent’ and ‘golden’, `bracket` defines the bracketing interval and can either have three items `(a, b, c)` so that `a < b < c` and `fun(b) < fun(a), fun(c)` or two items `a` and `c` which are assumed to be a starting interval for a downhill bracket search (see `bracket`); it doesn’t always mean that the obtained solution will satisfy `a <= x <= c`.

    bounds sequence, optional

      For method ‘bounded’, bounds is mandatory and must have two items corresponding to the optimization bounds.

    args tuple, optional

      Extra arguments passed to the objective function.

    method str or callable, optional

      Type of solver. Should be one of:

      > - ‘Brent’ (see here)

      > - ‘Bounded’ (see here)

      > - ‘Golden’ (see here)

      > - custom - a callable object (added in version 0.14.0), see below

    tol float, optional

      Tolerance for termination. For detailed control, use solver-specific options.

    options dict, optional

      A dictionary of solver options.

      > maxiterint

      >   Maximum number of iterations to perform.

      > dispbool

      >   Set to True to print convergence messages.

      See `show_options` for solver-specific options.

  Returns
    res OptimizeResult

      The optimization result represented as a `OptimizeResult` object. Important attributes are: `x` the solution array, `success` a Boolean flag indicating if the optimizer exited successfully and `message` which describes the cause of the termination. See `OptimizeResult` for a description of other attributes.

  See also

  `minimize`

    Interface to minimization algorithms for scalar multivariate functions

  `show_options`

    Additional options accepted by the solvers

  Notes

  This section describes the available solvers that can be selected by the ‘method’ parameter. The default method is Brent.

  Method Brent uses Brent’s algorithm to find a local minimum. The algorithm uses inverse parabolic interpolation when possible to speed up convergence of the golden section method.

  Method Golden uses the golden section search technique. It uses analog of the bisection method to decrease the bracketed interval. It is usually preferable to use the Brent method.

  Method Bounded can perform bounded minimization. It uses the Brent method to find a local minimum in the interval x1 < xopt < x2.

  Custom minimizers

  It may be useful to pass a custom minimization method, for example when using some library frontend to minimize_scalar. You can simply pass a callable as the `method` parameter.

  The callable is called as `method(fun, args, **kwargs, **options)` where `kwargs` corresponds to any other parameters passed to `minimize` (such as `bracket`, tol, etc.), except the options dict, which has its contents also passed as method parameters pair by pair. The method shall return an `OptimizeResult` object.

  The provided method callable must be able to accept (and possibly ignore) arbitrary parameters; the set of parameters accepted by `minimize` may expand in future versions and then these parameters will be passed to the method. You can find an example in the scipy.optimize tutorial.

  New in version 0.11.0.

  Examples

  Consider the problem of minimizing the following function.

      >>> def f(x):
      ...     return (x - 2) * x * (x + 2)**2

  Using the Brent method, we find the local minimum as:

      >>> from scipy.optimize import minimize_scalar
      >>> res = minimize_scalar(f)
      >>> res.x
      1.28077640403

  Using the Bounded method, we find a local minimum with specified bounds as:

      >>> res = minimize_scalar(f, bounds=(-3, -1), method='bounded')
      >>> res.x
      -2.0000002026

scipy.optimize.OptimizeWarning minimize_scalar(method=’brent’)