Dealing with Linear Constraints via Random Permutation

Dealing with Linear Constraints via Random Permutation

Simons Institute via YouTube Direct link

Theorem 2: a Pure Linear Algebra Problem

14 of 21

14 of 21

Theorem 2: a Pure Linear Algebra Problem

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Classroom Contents

Dealing with Linear Constraints via Random Permutation

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  1. 1 Intro
  2. 2 Optimization for Large-scale Problems
  3. 3 Go Beyond Unconstrained Optimization
  4. 4 Random Permutation Helps
  5. 5 Outline
  6. 6 Variants of multi-block ADMM
  7. 7 Apply Randomization Trick to ADMM
  8. 8 Summarize ADMM Variants
  9. 9 Numerical Experiments: Cyc-ADMM Often Diverges
  10. 10 Remarks on Divergence of Cyclic ADMM
  11. 11 Solve Linear System
  12. 12 Why Spectral Analysis?
  13. 13 Switched Linear System
  14. 14 Theorem 2: a Pure Linear Algebra Problem
  15. 15 Proof Sketch of Lemma 2
  16. 16 Interesting Byproduct: New Randomization Rule
  17. 17 Another Way to Apply Decomposition to Constraints
  18. 18 Comparison of Algorithms (cont'd)
  19. 19 Convergence Rate of Cyclic CD
  20. 20 Relation to Other Methods
  21. 21 Another variant of matrix AM-GM inequality

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