KSPQCG#

Code to run conjugate gradient method subject to a constraint on the solution norm [Ste83].

Options Database Key#

-ksp_qcg_trustregionradius - Trust Region Radius

Notes#

This is rarely used directly, ir is used in Trust Region methods for nonlinear equations, SNESNEWTONTR

Uses preconditioned conjugate gradient to compute an approximate minimizer of the quadratic function \( q(s) = g^T * s + .5 * s^T * H * s \) subject to the Euclidean norm trust region constraint \( || D * s || \le delta\), where

     delta is the trust region radius,
     g is the gradient vector, and
     H is Hessian matrix,
     D is a scaling matrix.

KSPConvergedReason may include

KSP_CONVERGED_NEG_CURVE - if convergence is reached along a negative curvature direction,
KSP_CONVERGED_STEP_LENGTH - if convergence is reached along a constrained step,

Note#

Allows symmetric preconditioning with the following scaling matrices#

      `PCNONE`:   D = Identity matrix
      `PCJACOBI`: D = diag [d_1, d_2, ...., d_n], where d_i = sqrt(H[i,i])
      `PCICC`:    D = L^T, implemented with forward and backward solves. Here L is an incomplete Cholesky factor of H.