Summer Graduate School
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Show List of Teaching Assistants
- Amitabh Basu
- Cynthia Vinzant (University of Washington)
Show List of Speakers
- Grigoriy Blekherman (Georgia Institute of Technology)
- Matthias Koeppe (University of California, Davis)
- Jiawang Nie (University of California, San Diego)
- Shmuel Onn
The workshop consists of four parts of lectures and corresponding tutorials and computer experimentation with computer software in the area.
Week 1 -- Schedule Week 1 (PDF)
The first part (Jiawang Nie, University of California, San Diego) introduces the basic theory of semidefinite programming, which includes convex sets and linear matrix inequalities, duality theory, optimality conditions, and applications such as in control and optimization. We will also introduce how to use the existing software for solving semidefinite programming problems.
Lecture Notes Week 1 Nie (PDF), Homework Assigments Week 1 (PDF)
The second part (Greg Blekherman, Virginia Tech) introduces positive polynomials, sum of squares, basic real algebraic geometry, and its connections to semidefinite programming. The applications will also be covered. Existing software will be introduced.
Lecture Notes Week 1 Blekherman (PDF)
Week 2 -- Schedule Week 2 (PDF)
The third part (Shmuel Onn, Technion - Israel Institute of Technology) concentrates on primal methods of integer linear and nonlinear optimization, such as the theory of test sets, in particular the recent advances in Graver basis methods.
The fourth part (Matthias Köppe, University of California, Davis) is on tools from the geometry of numbers, with a focus on rational generating function techniques for integer programming. We introduce lattices, the LLL algorithm, Lenstra's algorithm for integer programming in fixed dimension, Barvinok's theory of short rational generating functions, and the summation method for polynomial integer programming.
Lecture Notes Week 2 Koeppe (PDF)
Teaching assistants: Cynthia Vinzant, University of California, Berkeley and Amitabh Basu, University of California, Davis
Bibliography (PDF)
Bibliography 2 (PDF)
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Show Lodging
For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.
Show Directions to Venue
Show Visa/Immigration
Show Schedule, Notes/Handouts & Videos
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Aug 13, 2010 Friday |
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