# scipy.optimize.fmin¶

scipy.optimize.fmin(func, x0, args=(), xtol=0.0001, ftol=0.0001, maxiter=None, maxfun=None, full_output=0, disp=1, retall=0, callback=None)[source]

Minimize a function using the downhill simplex algorithm.

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). callback : callable, optional Called after each iteration, as callback(xk), where xk is the current parameter vector. xtol : float, optional Relative error in xopt acceptable for convergence. ftol : number, optional Relative error in func(xopt) 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. 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 1 : Maximum number of function evaluations made. 2 : Maximum number of iterations reached. allvecs : list Solution at each iteration.

See also

minimize
Interface to minimization algorithms for multivariate functions. See the ‘Nelder-Mead’ method in particular.

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.

References

 [R85] Nelder, J.A. and Mead, R. (1965), “A simplex method for function minimization”, The Computer Journal, 7, pp. 308-313
 [R86] Wright, M.H. (1996), “Direct Search Methods: Once Scorned, Now Respectable”, in Numerical Analysis 1995, Proceedings of the 1995 Dundee Biennial Conference in Numerical Analysis, D.F. Griffiths and G.A. Watson (Eds.), Addison Wesley Longman, Harlow, UK, pp. 191-208.

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