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"__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "", "annotation": "text", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Either None (for disp=True) or the text string (disp=False)" } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Show documentation for additional options of optimization solvers." } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "solver", "annotation": "str", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Type of optimization solver. One of 'minimize', 'minimize_scalar', 'root', 'root_scalar', 'linprog', or 'quadratic_assignment'." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "method", "annotation": "str, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "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')." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "disp", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Whether to print the result rather than returning it." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "These are method-specific options that can be supplied through the " }, { "__type": "InlineCode", "__tag": 4051, "value": "options" }, { "__type": "Text", "__tag": 4046, "value": " dict." } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "build-install/usr/lib/python3.14/site-packages/scipy/optimize/_optimize.py", "item_line": 3950, "item_type": "function", "aliases": [ "scipy.optimize.show_options" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "We can print documentations of a solver in stdout:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.optimize import show_options\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "show_options(solver=\"minimize\")\n", "execution_status": "failure", "out": "\n\nbfgs\n====\n\nMinimization of scalar function of one or more variables using the\nBFGS algorithm.\n\nOptions\n-------\ndisp : bool\n Set to True to print convergence messages.\nmaxiter : int\n Maximum number of iterations to perform.\ngtol : float\n Terminate successfully if gradient norm is less than `gtol`.\nnorm : float\n Order of norm (Inf is max, -Inf is min).\neps : float or ndarray\n If `jac is None` the absolute step size used for numerical\n approximation of the jacobian via forward differences.\nreturn_all : bool, optional\n Set to True to return a list of the best solution at each of the\n iterations.\nfinite_diff_rel_step : None or array_like, optional\n If ``jac in ['2-point', '3-point', 'cs']`` the relative step size to\n use for numerical approximation of the jacobian. The absolute step\n size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,\n possibly adjusted to fit into the bounds. For ``jac='3-point'``\n the sign of `h` is ignored. If None (default) then step is selected\n automatically.\nxrtol : float, default: 0\n Relative tolerance for `x`. Terminate successfully if step size is\n less than ``xk * xrtol`` where ``xk`` is the current parameter vector.\nc1 : float, default: 1e-4\n Parameter for Armijo condition rule.\nc2 : float, default: 0.9\n Parameter for curvature condition rule.\nhess_inv0 : None or ndarray, optional\n Initial inverse hessian estimate, shape (n, n). If None (default) then\n the identity matrix is used.\nworkers : int, map-like callable, optional\n A map-like callable, such as `multiprocessing.Pool.map` for evaluating\n any numerical differentiation in parallel.\n This evaluation is carried out as ``workers(fun, iterable)``.\n\n .. versionadded:: 1.16.0\n\nNotes\n-----\nParameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``.\n\nIf minimization doesn't complete successfully, with an error message of\n``Desired error not necessarily achieved due to precision loss``, then\nconsider setting `gtol` to a higher value. This precision loss typically\noccurs when the (finite difference) numerical differentiation cannot provide\nsufficient precision to satisfy the `gtol` termination criterion.\nThis can happen when working in single precision and a callable jac is not\nprovided. For single precision problems a `gtol` of 1e-3 seems to work.\n\ncg\n==\n\nMinimization of scalar function of one or more variables using the\nconjugate gradient algorithm.\n\nOptions\n-------\ndisp : bool\n Set to True to print convergence messages.\nmaxiter : int\n Maximum number of iterations to perform.\ngtol : float\n Gradient norm must be less than `gtol` before successful\n termination.\nnorm : float\n Order of norm (Inf is max, -Inf is min).\neps : float or ndarray\n If `jac is None` the absolute step size used for numerical\n approximation of the jacobian via forward differences.\nreturn_all : bool, optional\n Set to True to return a list of the best solution at each of the\n iterations.\nfinite_diff_rel_step : None or array_like, optional\n If ``jac in ['2-point', '3-point', 'cs']`` the relative step size to\n use for numerical approximation of the jacobian. The absolute step\n size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,\n possibly adjusted to fit into the bounds. For ``jac='3-point'``\n the sign of `h` is ignored. If None (default) then step is selected\n automatically.\nc1 : float, default: 1e-4\n Parameter for Armijo condition rule.\nc2 : float, default: 0.4\n Parameter for curvature condition rule.\nworkers : int, map-like callable, optional\n A map-like callable, such as `multiprocessing.Pool.map` for evaluating\n any numerical differentiation in parallel.\n This evaluation is carried out as ``workers(fun, iterable)``.\n\n .. versionadded:: 1.16.0\n\nNotes\n-----\nParameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``.\n\ncobyla\n======\n\nMinimize a scalar function of one or more variables using the\nConstrained Optimization BY Linear Approximation (COBYLA) algorithm.\nThis method uses the pure-python implementation of the algorithm from PRIMA.\n\nOptions\n-------\nrhobeg : float\n Reasonable initial changes to the variables.\ntol : float\n Final accuracy in the optimization (not precisely guaranteed).\n This is a lower bound on the size of the trust region.\ndisp : int\n Controls the frequency of output:\n 0. (default) There will be no printing\n 1. A message will be printed to the screen at the end of iteration, showing\n the best vector of variables found and its objective function value\n 2. in addition to 1, each new value of RHO is printed to the screen,\n with the best vector of variables so far and its objective function\n value.\n 3. in addition to 2, each function evaluation with its variables will\n be printed to the screen.\nmaxiter : int\n Maximum number of function evaluations.\ncatol : float\n Tolerance (absolute) for constraint violations\nf_target : float\n Stop if the objective function is less than `f_target`.\n\n .. versionchanged:: 1.16.0\n The original Powell implementation was replaced by a pure\n Python version from the PRIMA package, with bug fixes and\n improvements being made.\n\n\nReferences\n----------\nZhang Z. (2023), \"PRIMA: Reference Implementation for Powell's Methods with\nModernization and Amelioration\", https://www.libprima.net,\n:doi:`10.5281/zenodo.8052654`\n\ncobyqa\n======\n\nMinimize a scalar function of one or more variables using the\nConstrained Optimization BY Quadratic Approximations (COBYQA) algorithm [1]_.\n\n.. versionadded:: 1.14.0\n\nOptions\n-------\ndisp : bool\n Set to True to print information about the optimization procedure.\n Default is ``False``.\nmaxfev : int\n Maximum number of function evaluations. Default is ``500 * n``, where\n ``n`` is the number of variables.\nmaxiter : int\n Maximum number of iterations. Default is ``1000 * n``, where ``n`` is\n the number of variables.\nf_target : float\n Target value for the objective function. The optimization procedure is\n terminated when the objective function value of a feasible point (see\n `feasibility_tol` below) is less than or equal to this target. Default\n is ``-numpy.inf``.\nfeasibility_tol : float\n Absolute tolerance for the constraint violation. Default is ``1e-8``.\ninitial_tr_radius : float\n Initial trust-region radius. Typically, this value should be in the\n order of one tenth of the greatest expected change to the variables.\n Default is ``1.0``.\nfinal_tr_radius : float\n Final trust-region radius. It should indicate the accuracy required in\n the final values of the variables. If provided, this option overrides\n the value of `tol` in the `minimize` function. Default is ``1e-6``.\nscale : bool\n Set to True to scale the variables according to the bounds. If True and\n if all the lower and upper bounds are finite, the variables are scaled\n to be within the range :math:`[-1, 1]`. If any of the lower or upper\n bounds is infinite, the variables are not scaled. Default is ``False``.\n\nReferences\n----------\n.. [1] COBYQA\n https://www.cobyqa.com/stable/\n\ndogleg\n======\n\nMinimization of scalar function of one or more variables using\nthe dog-leg trust-region algorithm.\n\nOptions\n-------\ninitial_trust_radius : float\n Initial trust-region radius.\nmax_trust_radius : float\n Maximum value of the trust-region radius. No steps that are longer\n than this value will be proposed.\neta : float\n Trust region related acceptance stringency for proposed steps.\ngtol : float\n Gradient norm must be less than `gtol` before successful\n termination.\n\nl-bfgs-b\n========\n\nMinimize a scalar function of one or more variables using the L-BFGS-B\nalgorithm.\n\nOptions\n-------\nmaxcor : int\n The maximum number of variable metric corrections used to\n define the limited memory matrix. (The limited memory BFGS\n method does not store the full hessian but uses this many terms\n in an approximation to it.)\nftol : float\n The iteration stops when ``(f^k -\n f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol``.\ngtol : float\n The iteration will stop when ``max{|proj g_i | i = 1, ..., n}\n <= gtol`` where ``proj g_i`` is the i-th component of the\n projected gradient.\neps : float or ndarray\n If `jac is None` the absolute step size used for numerical\n approximation of the jacobian via forward differences.\nmaxfun : int\n Maximum number of function evaluations before minimization terminates.\n Note that this function may violate the limit if the gradients\n are evaluated by numerical differentiation.\nmaxiter : int\n Maximum number of algorithm iterations.\nmaxls : int, optional\n Maximum number of line search steps (per iteration). Default is 20.\nfinite_diff_rel_step : None or array_like, optional\n If ``jac in ['2-point', '3-point', 'cs']`` the relative step size to\n use for numerical approximation of the jacobian. The absolute step\n size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,\n possibly adjusted to fit into the bounds. For ``method='3-point'``\n the sign of `h` is ignored. If None (default) then step is selected\n automatically.\nworkers : int, map-like callable, optional\n A map-like callable, such as `multiprocessing.Pool.map` for evaluating\n any numerical differentiation in parallel.\n This evaluation is carried out as ``workers(fun, iterable)``.\n\n .. versionadded:: 1.16.0\n\nNotes\n-----\nThe option `ftol` is exposed via the `scipy.optimize.minimize` interface,\nbut calling `scipy.optimize.fmin_l_bfgs_b` directly exposes `factr`. The\nrelationship between the two is ``ftol = factr * numpy.finfo(float).eps``.\nI.e., `factr` multiplies the default machine floating-point precision to\narrive at `ftol`.\nIf the minimization is slow to converge the optimizer may halt if the\ntotal number of function evaluations exceeds `maxfun`, or the number of\nalgorithm iterations has reached `maxiter` (whichever comes first). If\nthis is the case then ``result.success=False``, and an appropriate\nerror message is contained in ``result.message``.\n\nnelder-mead\n===========\n\nMinimization of scalar function of one or more variables using the\nNelder-Mead algorithm.\n\nOptions\n-------\ndisp : bool\n Set to True to print convergence messages.\nmaxiter, maxfev : int\n Maximum allowed number of iterations and function evaluations.\n Will default to ``N*200``, where ``N`` is the number of\n variables, if neither `maxiter` or `maxfev` is set. If both\n `maxiter` and `maxfev` are set, minimization will stop at the\n first reached.\nreturn_all : bool, optional\n Set to True to return a list of the best solution at each of the\n iterations.\ninitial_simplex : array_like of shape (N + 1, N)\n Initial simplex. If given, overrides `x0`.\n ``initial_simplex[j,:]`` should contain the coordinates of\n the jth vertex of the ``N+1`` vertices in the simplex, where\n ``N`` is the dimension.\nxatol : float, optional\n Absolute error in xopt between iterations that is acceptable for\n convergence.\nfatol : number, optional\n Absolute error in func(xopt) between iterations that is acceptable for\n convergence.\nadaptive : bool, optional\n Adapt algorithm parameters to dimensionality of problem. Useful for\n high-dimensional minimization [1]_.\nbounds : sequence or `Bounds`, optional\n Bounds on variables. There are two ways to specify the bounds:\n\n 1. Instance of `Bounds` class.\n 2. Sequence of ``(min, max)`` pairs for each element in `x`. None\n is used to specify no bound.\n\n Note that this just clips all vertices in simplex based on\n the bounds.\n\nReferences\n----------\n.. [1] Gao, F. and Han, L.\n Implementing the Nelder-Mead simplex algorithm with adaptive\n parameters. 2012. Computational Optimization and Applications.\n 51:1, pp. 259-277\n\nnewton-cg\n=========\n\nMinimization of scalar function of one or more variables using the\nNewton-CG algorithm.\n\nNote that the `jac` parameter (Jacobian) is required.\n\nOptions\n-------\ndisp : bool\n Set to True to print convergence messages.\nxtol : float\n Average relative error in solution `xopt` acceptable for\n convergence.\nmaxiter : int\n Maximum number of iterations to perform.\neps : float or ndarray\n If `hessp` is approximated, use this value for the step size.\nreturn_all : bool, optional\n Set to True to return a list of the best solution at each of the\n iterations.\nc1 : float, default: 1e-4\n Parameter for Armijo condition rule.\nc2 : float, default: 0.9\n Parameter for curvature condition rule.\nworkers : int, map-like callable, optional\n A map-like callable, such as `multiprocessing.Pool.map` for evaluating\n any numerical differentiation in parallel.\n This evaluation is carried out as ``workers(fun, iterable)``.\n\n .. versionadded:: 1.16.0\n\nNotes\n-----\nParameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``.\n\npowell\n======\n\nMinimization of scalar function of one or more variables using the\nmodified Powell algorithm.\n\nParameters\n----------\nfun : callable\n The objective function to be minimized::\n\n fun(x, *args) -> float\n\n where ``x`` is a 1-D array with shape (n,) and ``args``\n is a tuple of the fixed parameters needed to completely\n specify the function.\nx0 : ndarray, shape (n,)\n Initial guess. Array of real elements of size (n,),\n where ``n`` is the number of independent variables.\nargs : tuple, optional\n Extra arguments passed to the objective function and its\n derivatives (`fun`, `jac` and `hess` functions).\nmethod : str or callable, optional\n The present documentation is specific to ``method='powell'``, but other\n options are available. See documentation for `scipy.optimize.minimize`.\nbounds : sequence or `Bounds`, optional\n Bounds on decision variables. There are two ways to specify the bounds:\n\n 1. Instance of `Bounds` class.\n 2. Sequence of ``(min, max)`` pairs for each element in `x`. None\n is used to specify no bound.\n\n If bounds are not provided, then an unbounded line search will be used.\n If bounds are provided and the initial guess is within the bounds, then\n every function evaluation throughout the minimization procedure will be\n within the bounds. If bounds are provided, the initial guess is outside\n the bounds, and `direc` is full rank (or left to default), then some\n function evaluations during the first iteration may be outside the\n bounds, but every function evaluation after the first iteration will be\n within the bounds. If `direc` is not full rank, then some parameters\n may not be optimized and the solution is not guaranteed to be within\n the bounds.\n\noptions : dict, optional\n A dictionary of solver options. All methods accept the following\n generic options:\n\n maxiter : int\n Maximum number of iterations to perform. Depending on the\n method each iteration may use several function evaluations.\n disp : bool\n Set to True to print convergence messages.\n\n See method-specific options for ``method='powell'`` below.\ncallback : callable, optional\n Called after each iteration. The signature is::\n\n callback(xk)\n\n where ``xk`` is the current parameter vector.\n\nReturns\n-------\nres : OptimizeResult\n The optimization result represented as a ``OptimizeResult`` object.\n Important attributes are: ``x`` the solution array, ``success`` a\n Boolean flag indicating if the optimizer exited successfully and\n ``message`` which describes the cause of the termination. See\n `OptimizeResult` for a description of other attributes.\n\nOptions\n-------\ndisp : bool\n Set to True to print convergence messages.\nxtol : float\n Relative error in solution `xopt` acceptable for convergence.\nftol : float\n Relative error in ``fun(xopt)`` acceptable for convergence.\nmaxiter, maxfev : int\n Maximum allowed number of iterations and function evaluations.\n Will default to ``N*1000``, where ``N`` is the number of\n variables, if neither `maxiter` or `maxfev` is set. If both\n `maxiter` and `maxfev` are set, minimization will stop at the\n first reached.\ndirec : ndarray\n Initial set of direction vectors for the Powell method.\nreturn_all : bool, optional\n Set to True to return a list of the best solution at each of the\n iterations.\n\nslsqp\n=====\n\nMinimize a scalar function of one or more variables using Sequential\nLeast Squares Programming (SLSQP).\n\nParameters\n----------\nftol : float\n Precision target for the value of f in the stopping criterion. This value\n controls the final accuracy for checking various optimality conditions;\n gradient of the lagrangian and absolute sum of the constraint violations\n should be lower than ``ftol``. Similarly, computed step size and the\n objective function changes are checked against this value. Default is 1e-6.\neps : float\n Step size used for numerical approximation of the Jacobian.\ndisp : bool\n Set to True to print convergence messages. If False,\n `verbosity` is ignored and set to 0.\nmaxiter : int, optional\n Maximum number of iterations. Default value is 100.\nfinite_diff_rel_step : None or array_like, optional\n If ``jac in ['2-point', '3-point', 'cs']`` the relative step size to\n use for numerical approximation of `jac`. The absolute step\n size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,\n possibly adjusted to fit into the bounds. For ``method='3-point'``\n the sign of `h` is ignored. If None (default) then step is selected\n automatically.\nworkers : int, map-like callable, optional\n A map-like callable, such as `multiprocessing.Pool.map` for evaluating\n any numerical differentiation in parallel.\n This evaluation is carried out as ``workers(fun, iterable)``.\n\n .. versionadded:: 1.16.0\n\nReturns\n-------\nres : OptimizeResult\n The optimization result represented as an `OptimizeResult` object.\n In this dict-like object the following fields are of particular importance:\n ``x`` the solution array, ``success`` a Boolean flag indicating if the\n optimizer exited successfully, ``message`` which describes the reason for\n termination, and ``multipliers`` which contains the Karush-Kuhn-Tucker\n (KKT) multipliers for the QP approximation used in solving the original\n nonlinear problem. See ``Notes`` below. See also `OptimizeResult` for a\n description of other attributes.\n\nNotes\n-----\nThe KKT multipliers are returned in the ``OptimizeResult.multipliers``\nattribute as a NumPy array. Denoting the dimension of the equality constraints\nwith ``meq``, and of inequality constraints with ``mineq``, then the returned\narray slice ``m[:meq]`` contains the multipliers for the equality constraints,\nand the remaining ``m[meq:meq + mineq]`` contains the multipliers for the\ninequality constraints. The multipliers corresponding to bound inequalities\nare not returned. See [1]_ pp. 321 or [2]_ for an explanation of how to interpret\nthese multipliers. The internal QP problem is solved using the methods given\nin [3]_ Chapter 25.\n\nNote that if new-style `NonlinearConstraint` or `LinearConstraint` were\nused, then ``minimize`` converts them first to old-style constraint dicts.\nIt is possible for a single new-style constraint to simultaneously contain\nboth inequality and equality constraints. This means that if there is mixing\nwithin a single constraint, then the returned list of multipliers will have\na different length than the original new-style constraints.\n\nReferences\n----------\n.. [1] Nocedal, J., and S J Wright, 2006, \"Numerical Optimization\", Springer,\n New York.\n.. [2] Kraft, D., \"A software package for sequential quadratic programming\",\n 1988, Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace Center, Germany.\n.. [3] Lawson, C. L., and R. J. Hanson, 1995, \"Solving Least Squares Problems\",\n SIAM, Philadelphia, PA.\n\ntnc\n===\n\nMinimize a scalar function of one or more variables using a truncated\nNewton (TNC) algorithm.\n\nOptions\n-------\neps : float or ndarray\n If `jac is None` the absolute step size used for numerical\n approximation of the jacobian via forward differences.\nscale : list of floats\n Scaling factors to apply to each variable. If None, the\n factors are up-low for interval bounded variables and\n 1+|x] for the others. Defaults to None.\noffset : float\n Value to subtract from each variable. If None, the\n offsets are (up+low)/2 for interval bounded variables\n and x for the others.\ndisp : bool\n Set to True to print convergence messages.\nmaxCGit : int\n Maximum number of hessian*vector evaluations per main\n iteration. If maxCGit == 0, the direction chosen is\n -gradient if maxCGit < 0, maxCGit is set to\n max(1,min(50,n/2)). Defaults to -1.\neta : float\n Severity of the line search. If < 0 or > 1, set to 0.25.\n Defaults to -1.\nstepmx : float\n Maximum step for the line search. May be increased during\n call. If too small, it will be set to 10.0. Defaults to 0.\naccuracy : float\n Relative precision for finite difference calculations. If\n <= machine_precision, set to sqrt(machine_precision).\n Defaults to 0.\nminfev : float\n Minimum function value estimate. Defaults to 0.\nftol : float\n Precision goal for the value of f in the stopping criterion.\n If ftol < 0.0, ftol is set to 0.0 defaults to -1.\nxtol : float\n Precision goal for the value of x in the stopping\n criterion (after applying x scaling factors). If xtol <\n 0.0, xtol is set to sqrt(machine_precision). Defaults to\n -1.\ngtol : float\n Precision goal for the value of the projected gradient in\n the stopping criterion (after applying x scaling factors).\n If gtol < 0.0, gtol is set to 1e-2 * sqrt(accuracy).\n Setting it to 0.0 is not recommended. Defaults to -1.\nrescale : float\n Scaling factor (in log10) used to trigger f value\n rescaling. If 0, rescale at each iteration. If a large\n value, never rescale. If < 0, rescale is set to 1.3.\nfinite_diff_rel_step : None or array_like, optional\n If ``jac in ['2-point', '3-point', 'cs']`` the relative step size to\n use for numerical approximation of the jacobian. The absolute step\n size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,\n possibly adjusted to fit into the bounds. For ``method='3-point'``\n the sign of `h` is ignored. If None (default) then step is selected\n automatically.\nmaxfun : int\n Maximum number of function evaluations. If None, `maxfun` is\n set to max(100, 10*len(x0)). Defaults to None.\nworkers : int, map-like callable, optional\n A map-like callable, such as `multiprocessing.Pool.map` for evaluating\n any numerical differentiation in parallel.\n This evaluation is carried out as ``workers(fun, iterable)``.\n\n .. versionadded:: 1.16.0\n\ntrust-ncg\n=========\n\nMinimization of scalar function of one or more variables using\nthe Newton conjugate gradient trust-region algorithm.\n\nOptions\n-------\ninitial_trust_radius : float\n Initial trust-region radius.\nmax_trust_radius : float\n Maximum value of the trust-region radius. No steps that are longer\n than this value will be proposed.\neta : float\n Trust region related acceptance stringency for proposed steps.\ngtol : float\n Gradient norm must be less than `gtol` before successful\n termination.\n\ntrust-constr\n============\n\nMinimize a scalar function subject to constraints.\n\nParameters\n----------\ngtol : float, optional\n Tolerance for termination by the norm of the Lagrangian gradient.\n The algorithm will terminate when both the infinity norm (i.e., max\n abs value) of the Lagrangian gradient and the constraint violation\n are smaller than ``gtol``. Default is 1e-8.\nxtol : float, optional\n Tolerance for termination by the change of the independent variable.\n The algorithm will terminate when ``tr_radius < xtol``, where\n ``tr_radius`` is the radius of the trust region used in the algorithm.\n Default is 1e-8.\nbarrier_tol : float, optional\n Threshold on the barrier parameter for the algorithm termination.\n When inequality constraints are present, the algorithm will terminate\n only when the barrier parameter is less than `barrier_tol`.\n Default is 1e-8.\nsparse_jacobian : {bool, None}, optional\n Determines how to represent Jacobians of the constraints. If bool,\n then Jacobians of all the constraints will be converted to the\n corresponding format. If None (default), then Jacobians won't be\n converted, but the algorithm can proceed only if they all have the\n same format.\ninitial_tr_radius: float, optional\n Initial trust radius. The trust radius gives the maximum distance\n between solution points in consecutive iterations. It reflects the\n trust the algorithm puts in the local approximation of the optimization\n problem. For an accurate local approximation the trust-region should be\n large and for an approximation valid only close to the current point it\n should be a small one. The trust radius is automatically updated throughout\n the optimization process, with ``initial_tr_radius`` being its initial value.\n Default is 1 (recommended in [1]_, p. 19).\ninitial_constr_penalty : float, optional\n Initial constraints penalty parameter. The penalty parameter is used for\n balancing the requirements of decreasing the objective function\n and satisfying the constraints. It is used for defining the merit function:\n ``merit_function(x) = fun(x) + constr_penalty * constr_norm_l2(x)``,\n where ``constr_norm_l2(x)`` is the l2 norm of a vector containing all\n the constraints. The merit function is used for accepting or rejecting\n trial points and ``constr_penalty`` weights the two conflicting goals\n of reducing objective function and constraints. The penalty is automatically\n updated throughout the optimization process, with\n ``initial_constr_penalty`` being its initial value. Default is 1\n (recommended in [1]_, p 19).\ninitial_barrier_parameter, initial_barrier_tolerance: float, optional\n Initial barrier parameter and initial tolerance for the barrier subproblem.\n Both are used only when inequality constraints are present. For dealing with\n optimization problems ``min_x f(x)`` subject to inequality constraints\n ``c(x) <= 0`` the algorithm introduces slack variables, solving the problem\n ``min_(x,s) f(x) + barrier_parameter*sum(ln(s))`` subject to the equality\n constraints ``c(x) + s = 0`` instead of the original problem. This subproblem\n is solved for decreasing values of ``barrier_parameter`` and with decreasing\n tolerances for the termination, starting with ``initial_barrier_parameter``\n for the barrier parameter and ``initial_barrier_tolerance`` for the\n barrier tolerance. Default is 0.1 for both values (recommended in [1]_ p. 19).\n Also note that ``barrier_parameter`` and ``barrier_tolerance`` are updated\n with the same prefactor.\nfactorization_method : str or None, optional\n Method to factorize the Jacobian of the constraints. Use None (default)\n for the auto selection or one of:\n\n - 'NormalEquation' (requires scikit-sparse)\n - 'AugmentedSystem'\n - 'QRFactorization'\n - 'SVDFactorization'\n\n The methods 'NormalEquation' and 'AugmentedSystem' can be used only\n with sparse constraints. The projections required by the algorithm\n will be computed using, respectively, the normal equation and the\n augmented system approaches explained in [1]_. 'NormalEquation'\n computes the Cholesky factorization of ``A A.T`` and 'AugmentedSystem'\n performs the LU factorization of an augmented system. They usually\n provide similar results. 'AugmentedSystem' is used by default for\n sparse matrices.\n\n The methods 'QRFactorization' and 'SVDFactorization' can be used\n only with dense constraints. They compute the required projections\n using, respectively, QR and SVD factorizations. The 'SVDFactorization'\n method can cope with Jacobian matrices with deficient row rank and will\n be used whenever other factorization methods fail (which may imply the\n conversion of sparse matrices to a dense format when required).\n By default, 'QRFactorization' is used for dense matrices.\nfinite_diff_rel_step : None or array_like, optional\n Relative step size for the finite difference approximation.\nmaxiter : int, optional\n Maximum number of algorithm iterations. Default is 1000.\nverbose : {0, 1, 2, 3}, optional\n Level of algorithm's verbosity:\n\n * 0 (default) : work silently.\n * 1 : display a termination report.\n * 2 : display progress during iterations.\n * 3 : display progress during iterations (more complete report).\n\ndisp : bool, optional\n If True (default), then `verbose` will be set to 1 if it was 0.\nworkers : int, map-like callable, optional\n A map-like callable, such as `multiprocessing.Pool.map` for evaluating\n any numerical differentiation in parallel.\n This evaluation is carried out as ``workers(fun, iterable)``.\n\n .. versionadded:: 1.16.0\n\nReturns\n-------\n`OptimizeResult` with the fields documented below. Note the following:\n\n 1. All values corresponding to the constraints are ordered as they\n were passed to the solver. And values corresponding to `bounds`\n constraints are put *after* other constraints.\n 2. All numbers of function, Jacobian or Hessian evaluations correspond\n to numbers of actual Python function calls. It means, for example,\n that if a Jacobian is estimated by finite differences, then the\n number of Jacobian evaluations will be zero and the number of\n function evaluations will be incremented by all calls during the\n finite difference estimation.\n\nx : ndarray, shape (n,)\n Solution found.\noptimality : float\n Infinity norm of the Lagrangian gradient at the solution.\nconstr_violation : float\n Maximum constraint violation at the solution.\nfun : float\n Objective function at the solution.\ngrad : ndarray, shape (n,)\n Gradient of the objective function at the solution.\nlagrangian_grad : ndarray, shape (n,)\n Gradient of the Lagrangian function at the solution.\nnit : int\n Total number of iterations.\nnfev : int\n Number of the objective function evaluations.\nnjev : int\n Number of the objective function gradient evaluations.\nnhev : int\n Number of the objective function Hessian evaluations.\ncg_niter : int\n Total number of the conjugate gradient method iterations.\nmethod : {'equality_constrained_sqp', 'tr_interior_point'}\n Optimization method used.\nconstr : list of ndarray\n List of constraint values at the solution.\njac : list of {ndarray, sparse array}\n List of the Jacobian matrices of the constraints at the solution.\nv : list of ndarray\n List of the Lagrange multipliers for the constraints at the solution.\n For an inequality constraint a positive multiplier means that the upper\n bound is active, a negative multiplier means that the lower bound is\n active and if a multiplier is zero it means the constraint is not\n active.\nconstr_nfev : list of int\n Number of constraint evaluations for each of the constraints.\nconstr_njev : list of int\n Number of Jacobian matrix evaluations for each of the constraints.\nconstr_nhev : list of int\n Number of Hessian evaluations for each of the constraints.\ntr_radius : float\n Radius of the trust region at the last iteration.\nconstr_penalty : float\n Penalty parameter at the last iteration, see `initial_constr_penalty`.\nbarrier_tolerance : float\n Tolerance for the barrier subproblem at the last iteration.\n Only for problems with inequality constraints.\nbarrier_parameter : float\n Barrier parameter at the last iteration. Only for problems\n with inequality constraints.\nexecution_time : float\n Total execution time.\nmessage : str\n Termination message.\nstatus : {0, 1, 2, 3, 4}\n Termination status:\n\n * 0 : The maximum number of function evaluations is exceeded.\n * 1 : `gtol` termination condition is satisfied.\n * 2 : `xtol` termination condition is satisfied.\n * 3 : `callback` raised `StopIteration`.\n * 4 : Constraint violation exceeds 'gtol'.\n\n .. versionchanged:: 1.15.0\n If the constraint violation exceeds `gtol`, then ``result.success``\n will now be False.\n\ncg_stop_cond : int\n Reason for CG subproblem termination at the last iteration:\n\n * 0 : CG subproblem not evaluated.\n * 1 : Iteration limit was reached.\n * 2 : Reached the trust-region boundary.\n * 3 : Negative curvature detected.\n * 4 : Tolerance was satisfied.\n\nReferences\n----------\n.. [1] Conn, A. R., Gould, N. I., & Toint, P. L.\n Trust region methods. 2000. Siam. pp. 19.\n\ntrust-exact\n===========\n\nMinimization of scalar function of one or more variables using\na nearly exact trust-region algorithm.\n\nOptions\n-------\ninitial_trust_radius : float\n Initial trust-region radius.\nmax_trust_radius : float\n Maximum value of the trust-region radius. No steps that are longer\n than this value will be proposed.\neta : float\n Trust region related acceptance stringency for proposed steps.\ngtol : float\n Gradient norm must be less than ``gtol`` before successful\n termination.\nsubproblem_maxiter : int, optional\n Maximum number of iterations to perform per subproblem. Only affects\n trust-exact. Default is 25.\n\n .. versionadded:: 1.17.0\n\ntrust-krylov\n============\n\nMinimization of a scalar function of one or more variables using\na nearly exact trust-region algorithm that only requires matrix\nvector products with the hessian matrix.\n\n.. versionadded:: 1.0.0\n\nOptions\n-------\ninexact : bool, optional\n Accuracy to solve subproblems. If True requires less nonlinear\n iterations, but more vector products.\n" }, { "__type": "Text", "__tag": 4046, "value": "\nSpecifying a method is possible:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "show_options(solver=\"minimize\", method=\"Nelder-Mead\")\n", "execution_status": "failure", "out": "Minimization of scalar function of one or more variables using the\nNelder-Mead algorithm.\n\nOptions\n-------\ndisp : bool\n Set to True to print convergence messages.\nmaxiter, maxfev : int\n Maximum allowed number of iterations and function evaluations.\n Will default to ``N*200``, where ``N`` is the number of\n variables, if neither `maxiter` or `maxfev` is set. If both\n `maxiter` and `maxfev` are set, minimization will stop at the\n first reached.\nreturn_all : bool, optional\n Set to True to return a list of the best solution at each of the\n iterations.\ninitial_simplex : array_like of shape (N + 1, N)\n Initial simplex. If given, overrides `x0`.\n ``initial_simplex[j,:]`` should contain the coordinates of\n the jth vertex of the ``N+1`` vertices in the simplex, where\n ``N`` is the dimension.\nxatol : float, optional\n Absolute error in xopt between iterations that is acceptable for\n convergence.\nfatol : number, optional\n Absolute error in func(xopt) between iterations that is acceptable for\n convergence.\nadaptive : bool, optional\n Adapt algorithm parameters to dimensionality of problem. Useful for\n high-dimensional minimization [1]_.\nbounds : sequence or `Bounds`, optional\n Bounds on variables. There are two ways to specify the bounds:\n\n 1. Instance of `Bounds` class.\n 2. Sequence of ``(min, max)`` pairs for each element in `x`. None\n is used to specify no bound.\n\n Note that this just clips all vertices in simplex based on\n the bounds.\n\nReferences\n----------\n.. [1] Gao, F. and Han, L.\n Implementing the Nelder-Mead simplex algorithm with adaptive\n parameters. 2012. Computational Optimization and Applications.\n 51:1, pp. 259-277\n" }, { "__type": "Text", "__tag": 4046, "value": "\nWe can also get the documentations as a string:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "show_options(solver=\"minimize\", method=\"Nelder-Mead\", disp=False)\n", "execution_status": "failure", "out": "'Minimization of scalar function of one or more variables using the\\nNelder-Mead algorithm.\\n\\nOptions\\n-------\\ndisp : bool\\n Set to True to print convergence messages.\\nmaxiter, maxfev : int\\n Maximum allowed number of iterations and function evaluations.\\n Will default to ``N*200``, where ``N`` is the number of\\n variables, if neither `maxiter` or `maxfev` is set. If both\\n `maxiter` and `maxfev` are set, minimization will stop at the\\n first reached.\\nreturn_all : bool, optional\\n Set to True to return a list of the best solution at each of the\\n iterations.\\ninitial_simplex : array_like of shape (N + 1, N)\\n Initial simplex. If given, overrides `x0`.\\n ``initial_simplex[j,:]`` should contain the coordinates of\\n the jth vertex of the ``N+1`` vertices in the simplex, where\\n ``N`` is the dimension.\\nxatol : float, optional\\n Absolute error in xopt between iterations that is acceptable for\\n convergence.\\nfatol : number, optional\\n Absolute error in func(xopt) between iterations that is acceptable for\\n convergence.\\nadaptive : bool, optional\\n Adapt algorithm parameters to dimensionality of problem. Useful for\\n high-dimensional minimization [1]_.\\nbounds : sequence or `Bounds`, optional\\n Bounds on variables. There are two ways to specify the bounds:\\n\\n 1. Instance of `Bounds` class.\\n 2. Sequence of ``(min, max)`` pairs for each element in `x`. None\\n is used to specify no bound.\\n\\n Note that this just clips all vertices in simplex based on\\n the bounds.\\n\\nReferences\\n----------\\n.. [1] Gao, F. and Han, L.\\n Implementing the Nelder-Mead simplex algorithm with adaptive\\n parameters. 2012. Computational Optimization and Applications.\\n 51:1, pp. 259-277'\n" } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "solver", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "method", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "disp", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "True" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "show_options" }, "references": null, "qa": "scipy.optimize._optimize:show_options", "arbitrary": [], "local_refs": [ "disp", "method", "solver" ] }