KSPQCG#

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

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 || <= 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 be

   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,

and other KSP converged/diverged reasons

Notes#

Currently we allow 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.

References#

  • **** -*** Trond Steihaug, The Conjugate Gradient Method and Trust Regions in Large Scale Optimization, SIAM Journal on Numerical Analysis, Vol. 20, No. 3 (Jun., 1983).

See Also#

KSP: Linear System Solvers, ‘KSPNASH, KSPGLTR, KSPSTCG, KSPCreate(), KSPSetType(), KSPType, KSP, KSPQCGSetTrustRegionRadius() KSPQCGGetTrialStepNorm(), KSPQCGGetQuadratic()`

Level#

developer

Location#

src/ksp/ksp/impls/qcg/qcg.c

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