minimize_scalar#
- scipy.optimize.minimize_scalar(fun, bracket=None, bounds=None, args=(), method=None, tol=None, options=None)[source]#
Local minimization of scalar function of one variable.
- Parameters:
- funcallable
Objective function. Scalar function, must return a scalar.
Suppose the callable has signature
f0(x, *my_args, **my_kwargs)
, wheremy_args
andmy_kwargs
are required positional and keyword arguments. Rather than passingf0
as the callable, wrap it to accept onlyx
; e.g., passfun=lambda x: f0(x, *my_args, **my_kwargs)
as the callable, wheremy_args
(tuple) andmy_kwargs
(dict) have been gathered before invoking this function.- bracketsequence, optional
For methods ‘brent’ and ‘golden’,
bracket
defines the bracketing interval and is required. Either a triple(xa, xb, xc)
satisfyingxa < xb < xc
andfunc(xb) < func(xa) and func(xb) < func(xc)
, or a pair(xa, xb)
to be used as initial points for a downhill bracket search (seescipy.optimize.bracket
). The minimizerres.x
will not necessarily satisfyxa <= res.x <= xb
.- boundssequence, optional
For method ‘bounded’, bounds is mandatory and must have two finite items corresponding to the optimization bounds.
- argstuple, optional
Extra arguments passed to the objective function.
- methodstr or callable, optional
Type of solver. Should be one of:
Default is “Bounded” if bounds are provided and “Brent” otherwise. See the ‘Notes’ section for details of each solver.
- tolfloat, optional
Tolerance for termination. For detailed control, use solver-specific options.
- optionsdict, 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:
- resOptimizeResult
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 andmessage
which describes the cause of the termination. SeeOptimizeResult
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 the
"Bounded"
Brent method if bounds are passed and unbounded"Brent"
otherwise.Method Brent uses Brent’s algorithm [1] 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 [1]. 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 [2] [3]. It uses the Brent method to find a local minimum in the interval x1 < xopt < x2.
Note that the Brent and Golden methods do not guarantee success unless a valid
bracket
triple is provided. If a three-point bracket cannot be found, considerscipy.optimize.minimize
. Also, all methods are intended only for local minimization. When the function of interest has more than one local minimum, consider Global optimization.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)
wherekwargs
corresponds to any other parameters passed tominimize
(such asbracket
, tol, etc.), except the options dict, which has its contents also passed as method parameters pair by pair. The method shall return anOptimizeResult
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.Added in version 0.11.0.
References
[1] (1,2)Press, W., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery. Numerical Recipes in C. Cambridge University Press.
[2]Forsythe, G.E., M. A. Malcolm, and C. B. Moler. “Computer Methods for Mathematical Computations.” Prentice-Hall Series in Automatic Computation 259 (1977).
[3]Brent, Richard P. Algorithms for Minimization Without Derivatives. Courier Corporation, 2013.
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.fun -9.9149495908
The minimizer is:
>>> 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.fun # minimum 3.28365179850e-13 >>> res.x # minimizer -2.0000002026