petscmain 20210420
KSPQCG
Code to run conjugate gradient method subject to a constraint on the solution norm. This is used in Trust Region methods for nonlinear equations, SNESNEWTONTR
Options Database Keys
 ksp_qcg_trustregionradius <r>   Trust Region Radius

Notes
This is rarely used directly
Notes
Use 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_CG_NEG_CURVE if convergence is reached along a negative curvature direction,
KSP_CONVERGED_CG_CONSTRAINED if convergence is reached along a constrained step,
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
 1.   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
KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPQCGSetTrustRegionRadius()
KSPQCGGetTrialStepNorm(), KSPQCGGetQuadratic()
Level
developer
Location
src/ksp/ksp/impls/qcg/qcg.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages