KSPNASH#

Code to run conjugate gradient method subject to a constraint on the solution norm in a trust region method [Nas84]

Options Database Keys#

  • -ksp_cg_radius - Trust Region Radius

Notes#

This is rarely used directly, it is used in Trust Region methods for nonlinear equations, SNESNEWTONTR

Uses 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

\[ || s || \le delta, \]

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 include

The preconditioner supplied must be symmetric and positive definite.

References#

Nas84

Stephen G Nash. Newton-type minimization via the Lanczos method. SIAM Journal on Numerical Analysis, 21(4):770–788, 1984.

See Also#

KSP: Linear System Solvers, KSPQCG, KSPGLTR, KSPSTCG, KSPCreate(), KSPSetType(), KSPType, KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn()

Level#

developer

Location#

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


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