KSPGLTR#

Code to run conjugate gradient method subject to a constraint on the solution norm, used within trust region methods [GLRT99]

Options Database Key#

  • -ksp_cg_radius - Trust Region Radius

Notes#

Uses preconditioned conjugate gradient to compute an approximate minimizer of the quadratic function

\[ q(s) = g^T * s + .5 * s^T * H * s \]

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,
     M is the positive definite preconditioner matrix.

KSPConvergedReason may have the additional values

The operator and the preconditioner supplied must be symmetric and positive definite.

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

References#

GLRT99

Nicholas IM Gould, Stefano Lucidi, Massimo Roma, and Philippe L Toint. Solving the trust-region subproblem using the lanczos method. SIAM Journal on Optimization, 9(2):504–525, 1999.

See Also#

KSP: Linear System Solvers, KSPQCG, KSPNASH, KSPSTCG, KSPCreate(), KSPSetType(), KSPType, KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn(), KSPGLTRGetMinEig(), KSPGLTRGetLambda(), KSPCG

Level#

developer

Location#

src/ksp/ksp/impls/cg/gltr/gltr.c


Index of all KSP routines
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Index of all manual pages