petsc-3.3-p7 2013-05-11

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, SNESTR

Options Database Keys

-ksp_nash_radius <r> -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.

KSPNASH

Options Database Keys

Notes

See Also