Summer Graduate School
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)
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A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.
A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.
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