CUTEstProblem.sphess

CUTEstProblem.sphess(x, v=None)

Evaluate sparse Hessian of objective or Lagrangian. For constrained problems, the Hessian is L_{x,x}(x,v).

# Hessian of objective (unconstrained problems)
H = problem.sphess(x)
# Hessian of Lagrangian (constrained problems)
H = problem.sphess(x, v)

For unconstrained problems, v must be None. For constrained problems, v must be specified. To evaluate the Hessian of the objective for constrained problems use isphess()

The matrix H is of type scipy.sparse.coo_matrix.

For small problems, problem.hess returns dense matrices.

This calls CUTEst routine CUTEST_csh or CUTEST_ush.

Note: in CUTEst, the sign convention is such that the Lagrangian = objective + lagrange_multipliers * constraints

Parameters:

• x (numpy.ndarray with shape (n,)) – input vector

• v (numpy.ndarray with shape (m,), optional) – vector of Lagrange multipliers (must be specified for constrained problems)

Returns:

sparse Hessian of objective (unconstrained) or Lagrangian (constrained) at x

Return type:

scipy.sparse.coo_matrix(n,n)