petsc-3.14.6 2021-03-30
KSPSTCG
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.
References
1. Steihaug, T. (1983): The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626--637
2. Toint, Ph.L. (1981): Towards an efficient sparsity exploiting Newton method for minimization. In: Duff, I., ed., Sparse Matrices and Their Uses, pp. 57--88. Academic Press
See Also
KSPCreate(), KSPCGSetType(), KSPType (for list of available types), KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn()
Level
developer
Location
src/ksp/ksp/impls/cg/stcg/stcg.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages