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

• KSP_CONVERGED_NEG_CURVE - if convergence is reached along a negative curvature direction,

• KSP_CONVERGED_STEP_LENGTH - if convergence is reached along a constrained step,

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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Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages