KSPSTCG#

Code to run conjugate gradient method subject to a constraint on the solution norm.

Options Database Keys#

  • -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 || <= 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_NEG_CURVE if convergence is reached along a negative curvature direction,
   KSP_CONVERGED_STEP_LENGTH if convergence is reached along a constrained step,

other KSP converged/diverged reasons

The preconditioner supplied should be symmetric and positive definite.

References#

  • **** -*** Steihaug, T. (1983): The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626–637

  • **** -*** 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#

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

Edit on GitLab

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