## CS 506, Computational Geometry, Spring 2020 |

- Jared Saia
- Email: "last name" at cs.unm.edu.
- Office: FEC 3120. The best way to reach me for this class is generally via Piazza. I check it every weekday, usually around noon.
- Office Hours: T/Th 1:45-3:00pm or by appointment.

- Convex Hull
- My Convex Hull Notes
- Jeff Erickson's Notes on Convex Hull
- Convex Crepes!
- High Dimensional Convex Hull; See also Quickhull
- Duality
- My Halfplane Intersection, Duality and Arrangements Notes
- UFL lecture notes on Duality
- U. Maryland Notes, Pages 41-44 give a good connection between convex hulls, and upper/lower envelopes, Lecture 8 gives good connection between envelopes and linear programming. Lecture 16 gives good connections between convex hulls and Voronoi diagrams, and Delaunay triangulations
- Voronoi Diagrams, Delaunay Triangulations and More Dual Transformations
- Linear Programming
- My notes on Linear Programming and High-Dimensional Convex Hulls
- Linear Programming: Gupta's notes, Lecture 17
- Higher Dimensional Spaces and Dimension Reduction
- My notes on Intro to Johnson-Lindenstrauss Projection
- My notes on advanced JL, epsilon-nets, and Applications
- My notes on the Singular Value Decomposition
- Arora Notes on Johnson-Lindenstrauss Projection
- You can embed an arbitrary metric into Euclidean space with O(log n) distortion (via Bourgain's theorem, see also here). Then, you can use Johnson-Lidenstrauss to project onto R^d where d = O(log n).
- Arora Notes on SVD (re low-rank approximation)
- Arora Notes on SVD (Part 2)
- Convex Optimization
- My notes on Multiplicative Weights Update (MWU) and learning under uncertainty
- Survey Paper on Multiplicative Weights Update by Arora et al.
- Online Convex Optimization via MWU (Section 3.9 of the Arora survey paper)
- Arora Lecture Notes on Gradient Descent and Stochastic Gradient Descent
- Boosting Intuition Video
- Boosting in Action!
- Class Summary

- Project Deliverable: The class project should be no more than 10 pages excluding bibliography and appendix; it can be 2 columns.
- More details on the class project and some project ideas are available here.
- MIT Algorithm's Projects This is a general description of how to find a good CS theory project. The specific project ideas in this class are, of course, different from our own class - if you'd like specific ideas, please talk to me.

- David Mount's Computational Geometry Notes The University of Maryland notes
- Sanjeev Arora Notes on Convex Optimization
- CS 506 - Spring 2017
- Blum, Hopcroft and Kannon Foundations of Data Science
- David Mount's Homework Problems The University of Maryland notes
- Suresh Venkatasubramanian's Comp. Geometry Class
- Convex Optimization Notes by Vishnoi Formal Treatment of Convex Optimization Algorithms
- MWU as Gradient Descent (Section 3):
- Convex Optimization by Boyd and Vandenberghe Particularly of interest: Section 2.3 "Operations that Preserve Convexity" ; Chapter 4 and onward discuss optimization algorithms (albeit informally, without proofs of convergence time; NB that many problems discussed (i.e. quadratic programming) are NP-Hard). See Vishnoi's notes above for a more formal treatment.