KSPGLTR#

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 + .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, 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#

Gould, N. and Lucidi, S. and Roma, M. and Toint, P., Solving the Trust-Region Subproblem using the Lanczos Method, SIAM Journal on Optimization, volume 9, number 2, 1999, 504-525

See Also#

KSPCreate(), KSPSetType(), KSPType, KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn(), KSPGLTRGetMinEig(), KSPGLTRGetLambda()

Level#

developer

Location#

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


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