Randomized Linear Algebra for Interior Point Methods

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Shows that predictor‑corrector IPMs retain their iteration complexity when each Newton linear system meets forward and backward error bounds (energy norm error ≤ δ) and δ ≤ ε/√n, and gives a cheap fix: compute an n‑vector correction vector v with ||v||2 = O(ε) to restore exact feasibility. Implementation uses a sketch‑based preconditioner (ADW + SVD/QR, à la Blendenpik/LSRN) and approximate solves with PCG; theory holds, experiments only on modest synthetic matrices.

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" chapters (14)

1. 0:00Introduction
2. 0:22Interior point methods background
3. 3:18Primal-dual LP formulation
4. 5:07Why interior point dominates
5. 8:02Central path navigation
6. 10:06Newton directions and updates
7. 11:56Predictor-corrector methods
8. 13:01Approximate solutions and errors
9. 15:31Feasibility correction with v
10. 17:58Augmented system comparison
11. 19:05Preconditioned conjugate gradient
12. 20:49Runtime complexity and preconditioners
13. 22:01Open problems
14. 24:25Q&A