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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_cg_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.

### Reference

Nash, Stephen G. Newton-type minimization via the Lanczos method. SIAM Journal on Numerical Analysis 21, no. 4 (1984): 770-788.

### See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn()

### 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