TAOADMM

Alternating direction method of multipliers method for solving linear problems with constraints. in a \( \min_x f(x) + g(z)\) s.t. \(Ax+Bz=c\). This algorithm employs two sub Tao solvers, of which type can be specified by the user. User need to provide ObjectiveAndGradient routine, and/or HessianRoutine for both subsolvers. Hessians can be given boolean flag determining whether they change with respect to a input vector. This can be set via TaoADMMSet{Misfit,Regularizer}HessianChangeStatus(). Second subsolver does support TAOSHELL. It should be noted that L1-norm is used for objective value for TAOSHELL type. There is option to set regularizer option, and currently soft-threshold is implemented. For spectral penalty update, currently there are basic option and adaptive option. Constraint is set at Ax+Bz=c, and A and B can be set with TaoADMMSet{Misfit,Regularizer}ConstraintJacobian(). c can be set with TaoADMMSetConstraintVectorRHS(). The user can also provide regularizer weight for second subsolver. [XFY+17]

Options Database Keys

• -tao_admm_regularizer_coefficient - regularizer constant (default 1.e-6)

• -tao_admm_spectral_penalty - Constant for Augmented Lagrangian term (default 1.)

• -tao_admm_relaxation_parameter - relaxation parameter for Z update (default 1.)

• -tao_admm_tolerance_update_factor - ADMM dynamic tolerance update factor (default 1.e-12)

• -tao_admm_spectral_penalty_update_factor - ADMM spectral penalty update curvature safeguard value (default 0.2)

• -tao_admm_minimum_spectral_penalty - Set ADMM minimum spectral penalty (default 0)

• -tao_admm_dual_update - Lagrangian dual update policy (“basic”,”adaptive”,”adaptive-relaxed”) (default “basic”)

• -tao_admm_regularizer_type - ADMM regularizer update rule (“user”,”soft-threshold”) (default “soft-threshold”)

References

[XFY+17]

Zheng Xu, Mario AT Figueiredo, Xiaoming Yuan, Christoph Studer, and Tom Goldstein. Adaptive relaxed ADMM: convergence theory and practical implementation. In Proceedings of the IEEE conference on computer vision and pattern recognition, 7389–7398. 2017.

See Also

TaoADMMSetMisfitHessianChangeStatus(), TaoADMMSetRegHessianChangeStatus(), TaoADMMGetSpectralPenalty(), TaoADMMGetMisfitSubsolver(), TaoADMMGetRegularizationSubsolver(), TaoADMMSetConstraintVectorRHS(), TaoADMMSetMinimumSpectralPenalty(), TaoADMMSetRegularizerCoefficient(), TaoADMMGetRegularizerCoefficient(), TaoADMMSetRegularizerConstraintJacobian(), TaoADMMSetMisfitConstraintJacobian(), TaoADMMSetMisfitObjectiveAndGradientRoutine(), TaoADMMSetMisfitHessianRoutine(), TaoADMMSetRegularizerObjectiveAndGradientRoutine(), TaoADMMSetRegularizerHessianRoutine(), TaoGetADMMParentTao(), TaoADMMGetDualVector(), TaoADMMSetRegularizerType(), TaoADMMGetRegularizerType(), TaoADMMSetUpdateType(), TaoADMMGetUpdateType()

Level

beginner

Location

src/tao/constrained/impls/admm/admm.c

Examples

src/tao/constrained/tutorials/tomographyADMM.c

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