petscmain 20210420
KSPGLTR
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_cg_radius <r>   Trust Region Radius

Notes
This is rarely used directly
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 trust region constraint
 s  <= delta,
where
delta is the trust region radius,
g is the gradient vector,
H is the Hessian approximation,
M is the positive definite preconditioner 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
The preconditioner supplied should be symmetric and positive definite.
Reference
Gould, N. and Lucidi, S. and Roma, M. and Toint, P., Solving the TrustRegion Subproblem using the Lanczos Method,
SIAM Journal on Optimization, volume 9, number 2, 1999, 504525
See Also
KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn(), KSPGLTRGetMinEig(), KSPGLTRGetLambda()
Level
developer
Location
src/ksp/ksp/impls/cg/gltr/gltr.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages