KSPQCG#

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

Options Database Key#

-ksp_qcg_trustregionradius r - Trust Region Radius

Notes#

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

Uses preconditioned conjugate gradient to compute an approximate minimizer of the quadratic function \(q(s) = g^T s + 0.5 s^T H s\) 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.