projected_cg(H, c, Z, Y, b, trust_radius=inf, lb=None, ub=None, tol=None, max_iter=None, max_infeasible_iter=None, return_all=False)

Solve equality-constrained quadratic programming problem min 1/2 x.T H x + x.t c subject to A x + b = 0 and, possibly, to trust region constraints ||x|| < trust_radius and box constraints lb <= x <= ub .

Notes

Implementation of Algorithm 6.2 on .

In the absence of spherical and box constraints, for sufficient iterations, the method returns a truly optimal result. In the presence of those constraints, the value returned is only a inexpensive approximation of the optimal value.

Parameters

H : LinearOperator (or sparse matrix or ndarray), shape (n, n)

Operator for computing H v .

c : array_like, shape (n,)

Gradient of the quadratic objective function.

Z : LinearOperator (or sparse matrix or ndarray), shape (n, n)

Operator for projecting x into the null space of A.

Y : LinearOperator, sparse matrix, ndarray, shape (n, m)

Operator that, for a given a vector b , compute smallest norm solution of A x + b = 0 .

b : array_like, shape (m,)

Right-hand side of the constraint equation.

trust_radius : float, optional

Trust radius to be considered. By default, uses trust_radius=inf , which means no trust radius at all.

lb : array_like, shape (n,), optional

Lower bounds to each one of the components of x . If lb[i] = -Inf the lower bound for the i-th component is just ignored (default).

ub : array_like, shape (n, ), optional

Upper bounds to each one of the components of x . If ub[i] = Inf the upper bound for the i-th component is just ignored (default).

tol : float, optional

Tolerance used to interrupt the algorithm.

max_iter : int, optional

Maximum algorithm iterations. Where max_inter <= n-m . By default, uses max_iter = n-m .

max_infeasible_iter : int, optional

Maximum infeasible (regarding box constraints) iterations the algorithm is allowed to take. By default, uses max_infeasible_iter = n-m .

return_all : bool, optional

When true , return the list of all vectors through the iterations.

Returns

x : array_like, shape (n,)

Solution of the EQP problem.

info : Dict

Dictionary containing the following:

Solve EQP problem with projected CG method.

Examples

See :

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GitHub : /scipy/optimize/_trustregion_constr/qp_subproblem.py#411
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