CUTEstProblem.hprod

CUTEstProblem.hprod(p, x=None, v=None)

Calculate Hessian-vector product H*p, where H is Hessian of objective (unconstrained) or Lagrangian (constrained). For constrained problems, the Hessian is L_{x,x}(x,v).

# use last computed Hessian to compute H*p
r = problem.hprod(p)
# use Hessian of Lagrangian L_{x,x}(x,v) to compute H*p (constrained only)
r = problem.hprod(p, x=x, v=v)
# use Hessian of objective at x to compute H*p (unconstrained only)
r = problem.hprod(p, x=x)

For unconstrained problems, v must be None. For constrained problems, v must be specified.

This calls CUTEst routine CUTEST_chprod or CUTEST_uhprod

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

Parameters:

  • p (numpy.ndarray with shape (n,)) – vector to be multiplied by the Hessian

  • x (numpy.ndarray with shape (n,), optional) – input vector for the Hessian

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

Returns:

Hessian-vector product H*p

Return type:

numpy.ndarray(n,)