Module « scipy.optimize »

Classe « NonlinearConstraint »

Informations générales

Héritage

builtins.object
    NonlinearConstraint

Définition

class NonlinearConstraint(builtins.object):

Description _{[extrait de NonlinearConstraint.__doc__]}

Nonlinear constraint on the variables.

    The constraint has the general inequality form::

        lb <= fun(x) <= ub

    Here the vector of independent variables x is passed as ndarray of shape
    (n,) and ``fun`` returns a vector with m components.

    It is possible to use equal bounds to represent an equality constraint or
    infinite bounds to represent a one-sided constraint.

    Parameters
    ----------
    fun : callable
        The function defining the constraint.
        The signature is ``fun(x) -> array_like, shape (m,)``.
    lb, ub : array_like
        Lower and upper bounds on the constraint. Each array must have the
        shape (m,) or be a scalar, in the latter case a bound will be the same
        for all components of the constraint. Use ``np.inf`` with an
        appropriate sign to specify a one-sided constraint.
        Set components of `lb` and `ub` equal to represent an equality
        constraint. Note that you can mix constraints of different types:
        interval, one-sided or equality, by setting different components of
        `lb` and `ub` as  necessary.
    jac : {callable,  '2-point', '3-point', 'cs'}, optional
        Method of computing the Jacobian matrix (an m-by-n matrix,
        where element (i, j) is the partial derivative of f[i] with
        respect to x[j]).  The keywords {'2-point', '3-point',
        'cs'} select a finite difference scheme for the numerical estimation.
        A callable must have the following signature:
        ``jac(x) -> {ndarray, sparse matrix}, shape (m, n)``.
        Default is '2-point'.
    hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy, None}, optional
        Method for computing the Hessian matrix. The keywords
        {'2-point', '3-point', 'cs'} select a finite difference scheme for
        numerical  estimation.  Alternatively, objects implementing
        `HessianUpdateStrategy` interface can be used to approximate the
        Hessian. Currently available implementations are:

            - `BFGS` (default option)
            - `SR1`

        A callable must return the Hessian matrix of ``dot(fun, v)`` and
        must have the following signature:
        ``hess(x, v) -> {LinearOperator, sparse matrix, array_like}, shape (n, n)``.
        Here ``v`` is ndarray with shape (m,) containing Lagrange multipliers.
    keep_feasible : array_like of bool, optional
        Whether to keep the constraint components feasible throughout
        iterations. A single value set this property for all components.
        Default is False. Has no effect for equality constraints.
    finite_diff_rel_step: None or array_like, optional
        Relative step size for the finite difference approximation. Default is
        None, which will select a reasonable value automatically depending
        on a finite difference scheme.
    finite_diff_jac_sparsity: {None, array_like, sparse matrix}, optional
        Defines the sparsity structure of the Jacobian matrix for finite
        difference estimation, its shape must be (m, n). If the Jacobian has
        only few non-zero elements in *each* row, providing the sparsity
        structure will greatly speed up the computations. A zero entry means
        that a corresponding element in the Jacobian is identically zero.
        If provided, forces the use of 'lsmr' trust-region solver.
        If None (default) then dense differencing will be used.

    Notes
    -----
    Finite difference schemes {'2-point', '3-point', 'cs'} may be used for
    approximating either the Jacobian or the Hessian. We, however, do not allow
    its use for approximating both simultaneously. Hence whenever the Jacobian
    is estimated via finite-differences, we require the Hessian to be estimated
    using one of the quasi-Newton strategies.

    The scheme 'cs' is potentially the most accurate, but requires the function
    to correctly handles complex inputs and be analytically continuable to the
    complex plane. The scheme '3-point' is more accurate than '2-point' but
    requires twice as many operations.

    Examples
    --------
    Constrain ``x[0] < sin(x[1]) + 1.9``

    >>> from scipy.optimize import NonlinearConstraint
    >>> con = lambda x: x[0] - np.sin(x[1])
    >>> nlc = NonlinearConstraint(con, -np.inf, 1.9)

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, fun, lb, ub, jac='2-point', hess=<scipy.optimize._hessian_update_strategy.BFGS object at 0x7f505a1095b0>, keep_feasible=False, finite_diff_rel_step=None, finite_diff_jac_sparsity=None)

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __hash__, __init_subclass__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__