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scipy.optimize.

# NonlinearConstraint

class scipy.optimize.NonlinearConstraint(fun, lb, ub, jac='2-point', hess=None, keep_feasible=False, finite_diff_rel_step=None, finite_diff_jac_sparsity=None)

  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 array}, 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 array, 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 sets 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 array}, 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
      >>> import numpy as np
      >>> con = lambda x: x[0] - np.sin(x[1])
      >>> nlc = NonlinearConstraint(con, -np.inf, 1.9)