Theory and Algorithms of Linear Matrix Inequalities

August 1 to August 5, 2005

at the

American Institute of Mathematics, San Jose, California

organized by

John Helton, Pablo A. Parrilo, and Mihai Putinar

Original Announcement

This workshop will be devoted to theoretical, practical and computational aspects of Linear Matrix Inequalities. Arguably, the biggest revolution in linear control theory in the 1990's has been the realization that most linear control problems convert directly to matrix inequalities. These take the form of a polynomial or rational function of matrices being positive semidefinite. The last few years have witnessed a fruitful and quite unexpected cross-polination, on this territory, of methods of real algebraic geometry, operator algebras, optimization theory and computation theory.

The workshop will bring together experts working in each one of these fields, with the aim of sharing their knowledge on a carefully selected set of genuinely interesting and new mathematical problems. The workshop will open very concrete possibilities of practical applications. The main topics for the workshop are

  1. Inequalities in a free *-algebra
  2. Computational real algebra (commutative or not)
  3. Determinantal representations of non-commutative polynomials

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Positive polynomials in scalar and matrix variables, the spectral theorem and optimization
by  J. William Helton and Mihai Putinar ,  Operator theory, structured matrices, and dilations, 229-306, Theta Ser. Adv. Math., 7, Theta, Bucharest, 2007  MR2389626