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 Keys

• -ksp_cg_radius radius - Trust Region Radius

• -ksp_cg_tr_norm_type (preconditioned|unpreconditioned) - Norm used for the trust-region constraint

Notes

This specializes KSPCG by enabling KSPSetConvergedNegativeCurvature() and selecting the unpreconditioned residual norm by default. All other options and APIs are shared with KSPCG. It is used in trust-region methods such as SNESNEWTONTR.

Use preconditioned conjugate gradient to compute an approximate minimizer of the quadratic function

\[ q(s) = g^T s + \frac{1}{2} s^T H s \]

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

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(), KSPCG, KSPCGSetType(), KSPType, KSP, KSPCGSetRadius(), KSPCGSetTRNormType(), KSPCGGetTRSolutionNorm(), KSPCGGetObjFcn(), KSPNASH, KSPGLTR, KSPQCG

Level

developer

Location

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

Examples

src/ksp/ksp/tests/ex94.c

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