petsc-3.12.4 2020-02-04
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# KSPSTCG

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.

### References

1. Steihaug, T. (1983): The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626–637 2. Toint, Ph.L. (1981): Towards an efficient sparsity exploiting Newton method for minimization. In: Duff, I., ed., Sparse Matrices and Their Uses, pp. 57–88. Academic Press

### See Also

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

### Level

developer

### Location

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