petsc-3.13.6 2020-09-29

TAOADMM

Alternating direction method of multipliers method fo 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 specificed 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 baisc 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.

References

1. -Xu, Zheng and Figueiredo, Mario A. T. and Yuan, Xiaoming and Studer, Christoph and Goldstein, Tom "Adaptive Relaxed ADMM: Convergence Theory and Practical Implementation" The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July, 2017.

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")

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

Level

beginner

Location

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

Examples