petsc-3.7.1 2016-05-15
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# 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, SNESNEWTONTR

### Options Database Keys

-ksp_nash_radius <r> -Trust Region Radius Many br

Notes: This is rarely used directly Many br

Many br

Use preconditioned conjugate gradient to compute Many bran approximate minimizer of the quadratic function Many br

q(s) = g^T * s + 0.5 * s^T * H * s Many br

subject to the trust region constraint Many br

|| s || <= delta, Many br

where Many br

delta is the trust region radius, Many brg is the gradient vector, Many brH is the Hessian approximation, and Many brM is the positive definite preconditioner matrix. Many br

KSPConvergedReason may be Many br

     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. Many br

### See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPNASHSetRadius(), KSPNASHGetNormD(), KSPNASHGetObjFcn()

Level:developer
Location:src/ksp/ksp/impls/cg/nash/nash.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages