Many practical algorithms in robotics, machine learning, and control can be understood as solutions to convex optimization problems. Knowing the mathematical and optimization structure behind these algorithms will deepen our understanding of them. Moreover, by recognizing underlying convex structure in his or her own research problems, the student can take advantage of some of the latest mathematical and software tools in optimization theory. This two-part seminar aims to cover several basic yet fundamental topics in convex optimization with a focus on applications to robotics, machine learning, and control. Part 1 of the course (Fall 2012, lead by Robert Platt) will introduce fundamental topics in convex optimization, polynomial optimization, and convex relaxations. Each of these topics will be explored in the context of important applications to robotics, machine learning, and control. Part 2 of the seminar (Spring 2013, lead by Hung Ngo) will cover algorithms for solving convex optimization problems with a focus on the relationship between the algorithms and problem structure.

Part I was lead by Robert Platt in the Fall of 2012.

In Part II, we will cover fundamental techniques and algorithms for formulating and solving optimization problems, including relaxation and rounding, randomized rounding, primal-dual method, interior point, simplex and eillipsoid methods, approximation algorithms, etc.

- free! The Design of Approximation Algorithms, David P. Williamson and David B. Shmoys. You can download the entire book for free.
- Nonlinear Programming, Dimitri P. Bertsekas. (Not free!) If there are materials covered in this book, I will give you some copies of chapters to read.

Familiarity with the materials covered in Part I of this seminar.

Each student will present 2 to 3 times per semester. The topics will be assigned.

The following books are helpful, though not required.

- Dimitri P. Bertsekas, Nonlinear Programming
- free! Stephen P. Boyd, Convex Optimization. (There is a free version)
- Vijay V. Vazirani, Approximation Algorithms
- David P. Williamson and David B. Shmoys, The Design of Approximation Algorithms
- Dorit Hochbaum, Approximation Algorithms for NP-Hard Problems
- Rajiv Motwani and Prabhakar Raghavan, Randomized Algorithms