SNESNEWTONTR

Newton based nonlinear solver that uses a trust-region strategy

Options Database Keys

• -snes_tr_deltamin deltamin - trust region parameter, minimum size of trust region

• -snes_tr_deltamax deltamax - trust region parameter, max size of trust region (default: 1e10)

• -snes_tr_delta0 delta0 - trust region parameter, initial size of trust region (default: 0.2)

• -snes_tr_eta1 eta1 - trust region parameter \(eta1 \le eta2\), \(rho > eta1\) breaks out of the inner iteration (default: 0.001)

• -snes_tr_eta2 eta2 - trust region parameter, \(rho \le eta2\) shrinks the trust region (default: 0.25)

• -snes_tr_eta3 eta3 - trust region parameter \(eta3 > eta2\), \(rho \ge eta3\) expands the trust region (default: 0.75)

• -snes_tr_t1 t1 - trust region parameter, shrinking factor of trust region (default: 0.25)

• -snes_tr_t2 t2 - trust region parameter, expanding factor of trust region (default: 2.0)

• -snes_tr_norm_type (1|2|infinity) - Type of norm for trust region bounds (default: 2)

• -snes_tr_fallback_type (newton,cauchy,dogleg) - Solution strategy to test reduction when step is outside of trust region. Can use scaled Newton direction, Cauchy point (Steepest Descent direction) or dogleg method.

Notes

The code is largely based on the book [NW06] and supports minimizing objective functions using a quadratic model. Quasi-Newton models are also supported.

Default step computation uses the Newton direction, but a dogleg type update is also supported. The 1- and infinity-norms are also supported, via SNESNewtonTRSetNormType(), when computing the trust region bounds.

References

[NW06]

Jorge Nocedal and Stephen Wright. Numerical optimization. Springer Science & Business Media, 2006.

See Also

SNES: Nonlinear Solvers, SNESCreate(), SNES, SNESSetType(), SNESSetObjective(), SNESNewtonTRSetTolerances(), SNESNewtonTRSetUpdateParameters(), SNESNewtonTRSetNormType(), SNESNewtonTRSetFallbackType(), SNESNewtonTRSetQNType(), SNESNewtonTRSetPostCheck(), SNESNewtonTRSetPreCheck()

Level

beginner

Location

src/snes/impls/tr/tr.c

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