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GRASP Seminar Series: Spring 2005
February 11, 11:00 AM, Levine Hall 307.
Pablo Parrilo
MIT
“Sum of Squares Programs: What are They Good For, and How To Solve Them”
Abstract: Sum of squares (SOS) programs are a particular class of convex optimization problems, that combine in a very appealing way notions from algebraic and numeric computation. They are based on the sum of squares decomposition for multivariate polynomials, and have found many interesting applications, mainly through semidefinite relaxations of polynomial optimization problems. In this talk we will discuss the basic SOS formulation, some important applications, as well as the techniques available for exploiting their special algebraic structure towards an efficient numerical solution. Additionally, we identify properties of systems of polynomial equations and inequalities that can be successfully exploited for numerical efficiency. The results will be motivated and illustrated through applications of sum of squares techniques from different areas, such as quantum information and systems and control theory.
Biography: Pablo A. Parrilo is Associate Professor in the Department of Electrical Engineering and Computer Science at MIT, and a member of the Laboratory for Information and Decision Systems (LIDS). His current research interests include control and identification of uncertain complex systems, robustness analysis and synthesis, and the development and application of computational tools based on convex optimization and algorithmic algebra to practically relevant problems in engineering, economics, and physics. From October 2001 through September 2004, Pablo was Assistant Professor of Analysis and Control Systems at the Automatic Control Laboratory of the Swiss Federal Institute of Technology (ETH Zurich). He received an Electronics Engineering degree from the University of Buenos Aires in 1994, a PhD in Control and Dynamical Systems from the California Institute of Technology in 2000, and held short-term visiting appointments at UC Santa Barbara, Lund Institute of Technology, and UC Berkeley.
