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, optional

Type of solver. Should be one of

  • ‘Brent’
  • ‘Bounded’
  • ‘Golden’

tol : float, optional

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

options : dict, optional

A dictionary of solver options.
xtol : float

Relative error in solution xopt acceptable for convergence.

maxiter : int

Maximum number of iterations to perform.

disp : bool

Set to True to print convergence messages.

Returns :

res : Result

The optimization result represented as a Result 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 Result for a description of other attributes.

See also

Interface to minimization algorithms for scalar multivariate functions.


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.


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

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

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

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