petsc-3.7.1 2016-05-15
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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 Many br

Notes: This is rarely used directly Many br

Many br

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

q(s) = g^T * s + .5 * s^T * H * s Many br

subject to the Euclidean norm trust region constraint Many br

|| D * s || <= delta, Many br

where Many br

delta is the trust region radius, Many brg is the gradient vector, and Many brH is Hessian matrix, Many brD is a scaling 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

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

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

### References

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

### See Also

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

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