`scipy.optimize._optimize:fmin`

source: /scipy/optimize/_optimize.py :575

Signature

   def     fmin (    func    ,    x0    ,    args    =  ()   ,    xtol    =  0.0001   ,    ftol    =  0.0001   ,    maxiter    =  None   ,    maxfun    =  None   ,    full_output    =  0   ,    disp    =  1   ,    retall    =  0   ,    callback    =  None   ,    initial_simplex    =  None     )

Summary

Minimize a function using the downhill simplex algorithm.

Extended Summary

This algorithm only uses function values, not derivatives or second derivatives.

Parameters

func : callable func(x,*args): The objective function to be minimized.
x0 : ndarray: Initial guess.
args : tuple, optional: Extra arguments passed to func, i.e., f(x,*args).
xtol : float, optional: Absolute error in xopt between iterations that is acceptable for convergence.
ftol : number, optional: Absolute error in func(xopt) between iterations that is acceptable for convergence.
maxiter : int, optional: Maximum number of iterations to perform.
maxfun : number, optional: Maximum number of function evaluations to make.
full_output : bool, optional: Set to True if fopt and warnflag outputs are desired.
disp : bool, optional: Set to True to print convergence messages.
retall : bool, optional: Set to True to return list of solutions at each iteration.
callback : callable, optional: Called after each iteration, as callback(xk), where xk is the current parameter vector.
initial_simplex : array_like of shape (N + 1, N), optional: Initial simplex. If given, overrides x0. initial_simplex[j,:] should contain the coordinates of the jth vertex of the N+1 vertices in the simplex, where N is the dimension.

Returns

xopt : ndarray: Parameter that minimizes function.
fopt : float: Value of function at minimum: fopt = func(xopt).
iter : int: Number of iterations performed.
funcalls : int: Number of function calls made.
warnflag : int: 1Maximum number of function evaluations made. 2 : Maximum number of iterations reached.
allvecs : list: Solution at each iteration.

Notes

Uses a Nelder-Mead simplex algorithm to find the minimum of function of one or more variables.

This algorithm has a long history of successful use in applications. But it will usually be slower than an algorithm that uses first or second derivative information. In practice, it can have poor performance in high-dimensional problems and is not robust to minimizing complicated functions. Additionally, there currently is no complete theory describing when the algorithm will successfully converge to the minimum, or how fast it will if it does. Both the ftol and xtol criteria must be met for convergence.

Examples

def f(x):
    return x**2

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from scipy import optimize

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minimum = optimize.fmin(f, 1)

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minimum[0]

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Aliases

scipy.optimize.fmin