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Alternating Direction Method of Multipliers ADMM

Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

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Page 1: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

Alternating Direction Method of Multipliers ADMM

Page 2: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

ADMM convergence

Page 3: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

ADMM scaled form

Page 4: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

Connection to prox operators

Page 5: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

Example: Lasso regression

Page 6: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM
Page 7: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM
Page 8: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

Practical issues

Page 9: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

Example: Sparse Subspace estimation

Page 10: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM
Page 11: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

Example: Low Rank + Sparse Decomposition

Page 12: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM
Page 13: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

Faster Convergence?

Page 14: Alternating Direction Method of Multipliers ADMMpradeepr/convexopt/Lecture_Slides/ADMM… · Under modest assumptions on f, g (these do not require A, B to be full rank), the ADMM

References