Minimize 1.0

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Minimization of scalar function of one variable.

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Parameters:

Parameters:	fun:callable Objective function.Scalar function, must return a scalar. bracket:sequence, optional For methods ‘brent’ and ‘golden’, `bracket` defines the bracketinginterval 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 downhillbracket search (see `bracket`); it doesn’t always mean that theobtained solution will satisfy `a<=x<=c`. bounds:sequence, optional For method ‘bounded’, bounds is mandatory and must have two itemscorresponding 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-specificoptions. 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` aBoolean flag indicating if the optimizer exited successfully and`message` which describes the cause of the termination. See`OptimizeResult` for a description of other attributes.

fun:callable

Objective function.Scalar function, must return a scalar.

bracket:sequence, optional

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

bounds:sequence, optional

For method ‘bounded’, bounds is mandatory and must have two itemscorresponding 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-specificoptions.

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 aBoolean flag indicating if the optimizer exited successfully andmessage which describes the cause of the termination. SeeOptimizeResult for a description of other attributes.

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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’salgorithm to find a local minimum. The algorithm uses inverseparabolic interpolation when possible to speed up convergence ofthe golden section method.

Method Golden uses thegolden section search technique. It uses analog of the bisectionmethod to decrease the bracketed interval. It is usuallypreferable to use the Brent method.

Method Bounded canperform bounded minimization. It uses the Brent method to find alocal minimum in the interval x1 < xopt < x2.

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Custom minimizers

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

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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 hasits contents also passed as method parameters pair by pair. The methodshall 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 mayexpand in future versions and then these parameters will be passed tothe method. You can find an example in the scipy.optimize tutorial.

Examples

Consider the problem of minimizing the following function.

Minimized 10 Letters

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

Minimize 1.0 Error

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

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Minimize 1.0 Error