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 - 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, KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn()

Level#

developer

Location#

src/ksp/ksp/impls/cg/nash/nash.c


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Index of all KSP routines
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Index of all manual pages