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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. Newton-type minimization via the Lanczos method. SIAM Journal on Numerical Analysis 21, no. 4 (1984): 770-788.

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