scipy.optimize.NonlinearConstraint¶

class
scipy.optimize.
NonlinearConstraint
(fun, lb, ub, jac='2point', hess=<scipy.optimize._hessian_update_strategy.BFGS object>, keep_feasible=False, finite_diff_rel_step=None, finite_diff_jac_sparsity=None)[source]¶ 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 onesided 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 onesided constraint. Set components of lb and ub equal to represent an equality constraint. Note that you can mix constraints of different types: interval, onesided or equality, by setting different components of lb and ub as necessary. jac : {callable, ‘2point’, ‘3point’, ‘cs’}, optional
Method of computing the Jacobian matrix (an mbyn matrix, where element (i, j) is the partial derivative of f[i] with respect to x[j]). The keywords {‘2point’, ‘3point’, ‘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 ‘2point’. hess : {callable, ‘2point’, ‘3point’, ‘cs’, HessianUpdateStrategy, None}, optional
Method for computing the Hessian matrix. The keywords {‘2point’, ‘3point’, ‘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: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)
. Herev
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 nonzero 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’ trustregion solver. If None (default) then dense differencing will be used.
Notes
Finite difference schemes {‘2point’, ‘3point’, ‘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 finitedifferences, we require the Hessian to be estimated using one of the quasiNewton 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 ‘3point’ is more accurate than ‘2point’ but requires twice as many operations.