(Topics are tentative. Code is updated on t-square.)

- 8/21, 8/23. Gradient descent. Notes (draft)
- to minimize , take step along gradient of .
- convex functions

- 8/28, 8/30. Faster Gradient descent, Newton method. Notes
- Take (near)-optimal step in gradient direction draft
- Newton-Raphson draft
- for root-finding:
- for optimization:

- 9/6,9/11. Projected (proximal) gradient descent. Notes (draft)
- take step along gradient; project to nearest feasible point.

- 9/13, 9/18, 9/25, 9/27. Solving linear systems
- 10/2,10/4,10/11. Singular Value Decomposition: .
- 10/16, 10/18, 10/25, 10/30. Linear programming (duality, simplex)
- Linear and Convex programming (ellipsoid, cutting plane, interior point)
- maintain minimum volume ellipsoid containing feasible half of previous ellipsoid. Notes (draft)
- separation oracles; maintain feasible polyhedron by adding cutting plane through violated point. Notes (draft)

- add smooth convex function to objective, minimize using Newton step. Notes (draft)

- Learning halfspaces: perceptron
- Matchings (maximum, weighted)
- find augmenting path; augment
- use linear program
- use cutting plane method: add violated blossom inequality; repeat

- Random walks, Brownian motion
- take random step from current point
- take infinitesimal random step

- Online optimization
- add random perturbation to objective, use offline optimization
- use gradient descent

- Stochastic gradient descent
- add random perturbation to objective (various options)

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