KSPSTCG

Code to run conjugate gradient method subject to a constraint on the solution norm for use in a trust region method [Ste83], [Toi81]

Options Database Key

• -ksp_cg_radius - Trust Region Radius

Notes

This is rarely used directly, it is used in Trust Region methods for nonlinear equations, SNESNEWTONTR

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

\[ || s || le delta, \]

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 include

• KSP_CONVERGED_NEG_CURVE - if convergence is reached along a negative curvature direction,

• KSP_CONVERGED_STEP_LENGTH - if convergence is reached along a constrained step,

The preconditioner supplied should be symmetric and positive definite.

References

[Ste83]

Trond Steihaug. The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal., 20:626–637, 1983.

[Toi81]

Philippe Toint. Towards an efficient sparsity exploiting Newton method for minimization. In Sparse matrices and their uses, pages 57–88. Academic press, 1981.

See Also

KSP: Linear System Solvers, KSPCreate(), KSPCGSetType(), KSPType, KSP, KSPCGSetRadius(), KSPCGGetNormD(), KSPCGGetObjFcn(), KSPNASH, KSPGLTR, KSPQCG

Level

developer

Location

src/ksp/ksp/impls/cg/stcg/stcg.c

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Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages