Interior Point Methods 4

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" summary

Claims an interior-point framework that gets sqrt(d) iterations while keeping each step as cheap as a projection-based Newton solve, yielding runtimes about input-size·sqrt(d) + d^{2.5} up to polylog factors. Method builds a regularized weighted log-barrier tied to a John-ellipse rounding, tracks both primal point and canonical constraint weights, estimates leverage-score diagonals with a leverage-score JL sketch, and uses fast linear-system solvers and sampling to make the scheme practical; the prototype analysis and algorithms succeed under these tools.

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" chapters (12)

1. 0:00Intro
2. 4:11The Picture
3. 4:44Standard Methods
4. 5:12Why Study Interior Point Methods (IPM)?
5. 6:58Two Key Ideas for Interior Point Methods
6. 19:50The Maximum Flow Problem
7. 28:16Recap: Path Following Methods
8. 30:19Path Following Analysis
9. 38:03Renegar's Algorithm
10. 41:42What's the Problem?
11. 48:02Regularized John Ellipse Barrier
12. 56:23Path Finding