Numerical optimization

Problem sheets:

Material about linear programming is covered in book by Jiří Matoušek and Bernd Gärtner Book Understanding and Using Linear Programming. Springer 2007. Also at. Below we will refer to this book by abbrewiation [MG]. Lecture notes

Lecture 1, first half
Lecture 1, second half: Introduction to linear programs, see [MG] Chapters 1, 2.2.
Lecture 2, Linear programming: basic feasible solutions, optimal solutions. [MG] Chapters 2.4, 2.7, 4.1, 4.2
Lecture 3: Simplex method, including pivot rules and exceptional cases. [MG] Chapter 5
Lecture 4: Convexity of sets and functions. Notes. See also Boyd and Vanderberghe Chapter 2.1.5.
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9
Lecture 14
Lecture 15

Example programs:

solving 3-SAT by optimization
denoising by Beck and Teboulle method

Additional references:

Notes by Nemirovski about self-concordance and interior point methods.
Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, Jonathan Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers copy
Neal Parikh, Stephen Boyd, Proximal Algorithms copy