scipy.optimize.show_options

scipy.optimize.show_options(solver=None, method=None)

Show documentation for additional options of optimization solvers.

These are method-specific options that can be supplied through the options dict.

Parameters:

solver : str

Type of optimization solver. One of ‘minimize’, ‘minimize_scalar’, ‘root’.

method : str, optional

If not given, shows all methods of the specified solver. Otherwise, show only the options for the specified method. Valid values corresponds to methods’ names of respective solver (e.g. ‘BFGS’ for ‘minimize’).

Notes

Minimize options

BFGS options:

gtol : float

Gradient norm must be less than gtol before successful termination.

norm : float

Order of norm (Inf is max, -Inf is min).

eps : float or ndarray

If jac is approximated, use this value for the step size.

Nelder-Mead options:

xtol : float

Relative error in solution xopt acceptable for convergence.

ftol : float

Relative error in fun(xopt) acceptable for convergence.

maxfev : int

Maximum number of function evaluations to make.

Newton-CG options:

xtol : float

Average relative error in solution xopt acceptable for convergence.

eps : float or ndarray

If jac is approximated, use this value for the step size.

CG options:

gtol : float

Gradient norm must be less than gtol before successful termination.

norm : float

Order of norm (Inf is max, -Inf is min).

eps : float or ndarray

If jac is approximated, use this value for the step size.

Powell options:

xtol : float

Relative error in solution xopt acceptable for convergence.

ftol : float

Relative error in fun(xopt) acceptable for convergence.

maxfev : int

Maximum number of function evaluations to make.

direc : ndarray

Initial set of direction vectors for the Powell method.

Anneal options:

ftol : float

Relative error in fun(x) acceptable for convergence.

schedule : str

Annealing schedule to use. One of: ‘fast’, ‘cauchy’ or ‘boltzmann’.

T0 : float

Initial Temperature (estimated as 1.2 times the largest cost-function deviation over random points in the range).

Tf : float

Final goal temperature.

maxfev : int

Maximum number of function evaluations to make.

maxaccept : int

Maximum changes to accept.

boltzmann : float

Boltzmann constant in acceptance test (increase for less stringent test at each temperature).

learn_rate : float

Scale constant for adjusting guesses.

quench, m, n : float

Parameters to alter fast_sa schedule.

lower, upper : float or ndarray

Lower and upper bounds on x.

dwell : int

The number of times to search the space at each temperature.

L-BFGS-B options:

ftol : float

The iteration stops when (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol.

gtol : float

The iteration will stop when max{|proj g_i | i = 1, ..., n} <= gtol where pg_i is the i-th component of the projected gradient.

maxcor : int

The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.)

maxiter : int

Maximum number of function evaluations.

TNC options:

ftol : float

Precision goal for the value of f in the stoping criterion. If ftol < 0.0, ftol is set to 0.0 defaults to -1.

xtol : float

Precision goal for the value of x in the stopping criterion (after applying x scaling factors). If xtol < 0.0, xtol is set to sqrt(machine_precision). Defaults to -1.

gtol : float

Precision goal for the value of the projected gradient in the stopping criterion (after applying x scaling factors). If gtol < 0.0, gtol is set to 1e-2 * sqrt(accuracy). Setting it to 0.0 is not recommended. Defaults to -1.

scale : list of floats

Scaling factors to apply to each variable. If None, the factors are up-low for interval bounded variables and 1+|x] fo the others. Defaults to None

offset : float

Value to subtract from each variable. If None, the offsets are (up+low)/2 for interval bounded variables and x for the others.

maxCGit : int

Maximum number of hessian*vector evaluations per main iteration. If maxCGit == 0, the direction chosen is -gradient if maxCGit < 0, maxCGit is set to max(1,min(50,n/2)). Defaults to -1.

maxiter : int

Maximum number of function evaluation. if None, maxiter is set to max(100, 10*len(x0)). Defaults to None.

eta : float

Severity of the line search. if < 0 or > 1, set to 0.25. Defaults to -1.

stepmx : float

Maximum step for the line search. May be increased during call. If too small, it will be set to 10.0. Defaults to 0.

accuracy : float

Relative precision for finite difference calculations. If <= machine_precision, set to sqrt(machine_precision). Defaults to 0.

minfev : float

Minimum function value estimate. Defaults to 0.

rescale : float

Scaling factor (in log10) used to trigger f value rescaling. If 0, rescale at each iteration. If a large value, never rescale. If < 0, rescale is set to 1.3.

COBYLA options:

tol : float

Final accuracy in the optimization (not precisely guaranteed). This is a lower bound on the size of the trust region.

rhobeg : float

Reasonable initial changes to the variables.

maxfev : int

Maximum number of function evaluations.

catol : float

Absolute tolerance for constraint violations (default: 1e-6).

SLSQP options:

ftol : float

Precision goal for the value of f in the stopping criterion.

eps : float

Step size used for numerical approximation of the jacobian.

maxiter : int

Maximum number of iterations.

dogleg options:

initial_trust_radius : float

Initial trust-region radius.

max_trust_radius : float

Maximum value of the trust-region radius. No steps that are longer than this value will be proposed.

eta : float

Trust region related acceptance stringency for proposed steps.

gtol : float

Gradient norm must be less than gtol before successful termination.

trust-ncg options:

See dogleg options.

minimize_scalar options

brent options:

xtol : float

Relative error in solution xopt acceptable for convergence.

bounded options:

xatol : float

Absolute error in solution xopt acceptable for convergence.

golden options:

xtol : float

Relative error in solution xopt acceptable for convergence.

root options

hybrd options:

col_deriv : bool

Specify whether the Jacobian function computes derivatives down the columns (faster, because there is no transpose operation).

xtol : float

The calculation will terminate if the relative error between two consecutive iterates is at most xtol.

maxfev : int

The maximum number of calls to the function. If zero, then 100*(N+1) is the maximum where N is the number of elements in x0.

band : sequence

If set to a two-sequence containing the number of sub- and super-diagonals within the band of the Jacobi matrix, the Jacobi matrix is considered banded (only for fprime=None).

epsfcn : float

A suitable step length for the forward-difference approximation of the Jacobian (for fprime=None). If epsfcn is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision.

factor : float

A parameter determining the initial step bound (factor * || diag * x||). Should be in the interval (0.1, 100).

diag : sequence

N positive entries that serve as a scale factors for the variables.

LM options:

col_deriv : bool

non-zero to specify that the Jacobian function computes derivatives down the columns (faster, because there is no transpose operation).

ftol : float

Relative error desired in the sum of squares.

xtol : float

Relative error desired in the approximate solution.

gtol : float

Orthogonality desired between the function vector and the columns of the Jacobian.

maxiter : int

The maximum number of calls to the function. If zero, then 100*(N+1) is the maximum where N is the number of elements in x0.

epsfcn : float

A suitable step length for the forward-difference approximation of the Jacobian (for Dfun=None). If epsfcn is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision.

factor : float

A parameter determining the initial step bound (factor * || diag * x||). Should be in interval (0.1, 100).

diag : sequence

N positive entries that serve as a scale factors for the variables.

Broyden1 options:

nit : int, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

disp : bool, optional

Print status to stdout on every iteration.

maxiter : int, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftol : float, optional

Relative tolerance for the residual. If omitted, not used.

fatol : float, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtol : float, optional

Relative minimum step size. If omitted, not used.

xatol : float, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_norm : function(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_options : dict, optional

Options for the respective Jacobian approximation.

alpha : float, optional

Initial guess for the Jacobian is (-1/alpha).

reduction_method : str or tuple, optional

Method used in ensuring that the rank of the Broyden matrix stays low. Can either be a string giving the name of the method, or a tuple of the form (method, param1, param2, ...) that gives the name of the method and values for additional parameters.

Methods available:

• restart: drop all matrix columns. Has no

  extra parameters.

• simple: drop oldest matrix column. Has no

  extra parameters.

• svd: keep only the most significant SVD

  components.

  Extra parameters:

  • ``to_retain`: number of SVD components to

    retain when rank reduction is done. Default is max_rank - 2.

max_rank : int, optional

Maximum rank for the Broyden matrix. Default is infinity (ie., no rank reduction).

Broyden2 options:

nit : int, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

disp : bool, optional

Print status to stdout on every iteration.

maxiter : int, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftol : float, optional

Relative tolerance for the residual. If omitted, not used.

fatol : float, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtol : float, optional

Relative minimum step size. If omitted, not used.

xatol : float, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_norm : function(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_options : dict, optional

Options for the respective Jacobian approximation.

alpha : float, optional

Initial guess for the Jacobian is (-1/alpha).

reduction_method : str or tuple, optional

Method used in ensuring that the rank of the Broyden matrix stays low. Can either be a string giving the name of the method, or a tuple of the form (method, param1, param2, ...) that gives the name of the method and values for additional parameters.

Methods available:

• restart: drop all matrix columns. Has no

  extra parameters.

• simple: drop oldest matrix column. Has no

  extra parameters.

• svd: keep only the most significant SVD

  components.

  Extra parameters:

  • ``to_retain`: number of SVD components to

    retain when rank reduction is done. Default is max_rank - 2.

max_rank : int, optional

Maximum rank for the Broyden matrix. Default is infinity (ie., no rank reduction).

Anderson options:

nit : int, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

disp : bool, optional

Print status to stdout on every iteration.

maxiter : int, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftol : float, optional

Relative tolerance for the residual. If omitted, not used.

fatol : float, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtol : float, optional

Relative minimum step size. If omitted, not used.

xatol : float, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_norm : function(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_options : dict, optional

Options for the respective Jacobian approximation.

alpha : float, optional

Initial guess for the Jacobian is (-1/alpha).

M : float, optional

Number of previous vectors to retain. Defaults to 5.

w0 : float, optional

Regularization parameter for numerical stability. Compared to unity, good values of the order of 0.01.

LinearMixing options:

nit : int, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

disp : bool, optional

Print status to stdout on every iteration.

maxiter : int, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftol : float, optional

Relative tolerance for the residual. If omitted, not used.

fatol : float, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtol : float, optional

Relative minimum step size. If omitted, not used.

xatol : float, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_norm : function(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_options : dict, optional

Options for the respective Jacobian approximation.

alpha : float, optional

initial guess for the jacobian is (-1/alpha).

DiagBroyden options:

nit : int, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

disp : bool, optional

Print status to stdout on every iteration.

maxiter : int, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftol : float, optional

Relative tolerance for the residual. If omitted, not used.

fatol : float, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtol : float, optional

Relative minimum step size. If omitted, not used.

xatol : float, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_norm : function(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_options : dict, optional

Options for the respective Jacobian approximation.

alpha : float, optional

initial guess for the jacobian is (-1/alpha).

ExcitingMixing options:

nit : int, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

disp : bool, optional

Print status to stdout on every iteration.

maxiter : int, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftol : float, optional

Relative tolerance for the residual. If omitted, not used.

fatol : float, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtol : float, optional

Relative minimum step size. If omitted, not used.

xatol : float, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_norm : function(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_options : dict, optional

Options for the respective Jacobian approximation.

alpha : float, optional

Initial Jacobian approximation is (-1/alpha).

alphamax : float, optional

The entries of the diagonal Jacobian are kept in the range [alpha, alphamax].

Krylov options:

nit : int, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

disp : bool, optional

Print status to stdout on every iteration.

maxiter : int, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftol : float, optional

Relative tolerance for the residual. If omitted, not used.

fatol : float, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtol : float, optional

Relative minimum step size. If omitted, not used.

xatol : float, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_norm : function(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_options : dict, optional

Options for the respective Jacobian approximation.

rdiff : float, optional

Relative step size to use in numerical differentiation.

method : {‘lgmres’, ‘gmres’, ‘bicgstab’, ‘cgs’, ‘minres’} or function

Krylov method to use to approximate the Jacobian. Can be a string, or a function implementing the same interface as the iterative solvers in scipy.sparse.linalg.

The default is scipy.sparse.linalg.lgmres.

inner_M : LinearOperator or InverseJacobian

Preconditioner for the inner Krylov iteration. Note that you can use also inverse Jacobians as (adaptive) preconditioners. For example,

>>> jac = BroydenFirst()
>>> kjac = KrylovJacobian(inner_M=jac.inverse).

If the preconditioner has a method named ‘update’, it will be called as update(x, f) after each nonlinear step, with x giving the current point, and f the current function value.

inner_tol, inner_maxiter, ...

Parameters to pass on to the “inner” Krylov solver. See scipy.sparse.linalg.gmres for details.

outer_k : int, optional

Size of the subspace kept across LGMRES nonlinear iterations.

See scipy.sparse.linalg.lgmres for details.