petscmaster 20201129
KSPNASH
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 + 0.5 * 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, and
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
Nash, Stephen G. Newtontype minimization via the Lanczos method. SIAM Journal on Numerical Analysis 21, no. 4 (1984): 770788.
See Also
KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn()
Level
developer
Location
src/ksp/ksp/impls/cg/nash/nash.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages