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
- 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 Trust-Region Subproblem using the Lanczos Method, SIAM Journal on Optimization, volume 9, number 2, 1999, 504-525
See Also#
KSPCreate()
, KSPSetType()
, KSPType
, 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