**-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 + .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 (for list of available types), KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn(), KSPGLTRGetMinEig(), KSPGLTRGetLambda()

### Level

developer

### Location

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

Index of all KSP routines

Table of Contents for all manual pages

Index of all manual pages