The Tutorial Workshop:

Linear Matrix Inequalities and Polynomial Optimization (LMIPO)

Mathematics Department (AP&M 6402), UCSD, March 22-25, 2010

Organizers: Jiawang Nie, and Bill Helton

Theme of LMIPO

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)
  • Topics of LMIPO

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

    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.
  • Participants

  • 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)
  • Applications

    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).

    The deadline of the application is November 30, 2009.

    Hotel Accommodations

    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.

    Contact Information

        Jiawang Nie (njw AT
        Bill Helton (helton AT
      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.