petsc-3.12.4 2020-02-04
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# KSPQCG

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_qcg_trustregionradius <r> -Trust Region Radius

### Notes

This is rarely used directly

### Notes

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 Euclidean norm trust region constraint

|| D * s || <= delta,

where

delta is the trust region radius, g is the gradient vector, and H is Hessian matrix, D is a scaling 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

### Currently we allow symmetric preconditioning with the following scaling matrices

PCNONE: D = Identity matrix PCJACOBI: D = diag [d_1, d_2, ...., d_n], where d_i = sqrt(H[i,i]) PCICC: D = L^T, implemented with forward and backward solves. Here L is an incomplete Cholesky factor of H.

### References

1. -Trond Steihaug, The Conjugate Gradient Method and Trust Regions in Large Scale Optimization, SIAM Journal on Numerical Analysis, Vol. 20, No. 3 (Jun., 1983).

### See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPQCGSetTrustRegionRadius()
KSPQCGGetTrialStepNorm(), KSPQCGGetQuadratic()

### Level

developer

### Location

src/ksp/ksp/impls/qcg/qcg.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages