- Polynomial optimization is an important topic in mathematical programming theory and applications. It is often NP-hard. Recently, linear matrix inequality and semidefinite programming techqniues prove very efficient in finding global optimal solution for polynomial optimization problems. They bring interesting interations between mathematical areas like convex analysis, optimization theory, moment theory, and algebraic geometry. This workshop will be an introduction to the mathematical tools required to do research in this area. Little background is required; indeed the tutorials will be understandable to graduate students.

Pablo Parrilo (MIT) Mihai Putinar (UCSB) Bernd Sturmfels (UC Berkeley) Rekha Thomas (Univ. Washington)

Linear Matrix Inequalities Semidefinite Programming Sum of Squares and Nonnegative Polynomials Geometry of Spectrahedra Positivstellensatz and Moment Theory

Here is the lecture program. All the lectures and discussions will be held in 6402 of Applied Physics and Mathematics Building where the Mathematics Departemnt is located.

The following are the assignments by lecturers:pwd

Assignments by Prof. Parrilo. Assignments by Prof. Putinar. Assignments by Prof. Sturmfels (Solution) . Assignments by Prof. Thomas.

Amir Ali Ahmadi (MIT) Robert Boneau (Air Force) Chung-Ching Chang (Stanford) Venkat Chandrasekaran (MIT) Jerry Cruz (Caltech) Maria Angelica Cueto (Berkeley) Onkar Dalal (Stanford) Dmitriy Drusvyatskiy (Cornell) Laura Escobar (SFSU) Dennice Gayme (Caltech) Benjamin Iriarte Giraldo (SFSU) Laurent Lessard (Stanford) Mert Gurbuzbalaban (NYU) Martin Harrison (UCSB) Joohee Hong (UC Davis) Na Li (Caltech) Qihang Lin (CMU) Matt Low (UC Davis) Ha Nguyen (Emory)Mohamed Omar (UC Davis) James Pfeiffer (Univ. Washington) Dzung Phan (Univ. Florida) Cordian Riener (Frankfurt) Felipe Rincon (Berkeley) Parikshit Shah (MIT) Hyung Sik (Stanford) Sudhanshu Singh (UNC) Richard Spjut (UCSB) Noah D. Stein (MIT) Antonios Varvitsiotis (CWI) Yang Wang (Stanford) Qiu Wu (UT-Austin) Hongchao Zhang (LSU) Yi Zhang (LSU) Jeremy Greene (UCSD) Chris Nelson (UCSD) Li Wang (UCSD)

This tutorial workshop is funded by NSF Grant DMS-0844775.

Limited financial supports are available for student participants who need travel support. Interesting students needing financial supports please apply by sending email to Jiawang Nie. In the email, please indicate the applicant's name, institution and department, research area, the name and email address of the student's advisor (who we possibly will contact).

Thedeadlineof the application is November 30, 2009.

Hotel reservations have been reserved in Residence Inn for student participants.

Address: 8901 Gilman Drive, La Jolla, CA 92037.

Contact phone: (858) 587-1770, (800)454-4361

For those participants whose hotel reservation is not made through the workshop organizers, there are other hotels in La Jolla area. They usually have special rates for UCSD visitors. Please mention you are going to attend a workshop in UCSD to get the special rates.

Organizer: Jiawang Nie (njw AT math.ucsd.edu) Co-Organizer: Bill Helton (helton AT math.ucsd.edu) Mailing address: Jiawang Nie UCSD Mathematics Department 9500 Gilman Drive La Jolla, CA 92093 Phone number: (858)534-6015

This tutorial workshop is funded by NSF project "CAREER: Linear Matrix Inequality Representations in Optimization"DMS-0844775, and also under the help of NSF Project "FRG: Collaborative Research: Semidefinite optimization and convex algebraic geometry" DMS-0757212.