SciPy

scipy.optimize.minimize_scalar

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

Minimization of scalar function of one variable.

New in version 0.11.0.

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’
  • ‘Bounded’
  • ‘Golden’
  • custom - a callable object (added in version 0.14.0)

tol : float, optional

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

options : dict, optional

A dictionary of solver options.
maxiter : int

Maximum number of iterations to perform.

disp : bool

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.

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