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”)



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()







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