Abstract: Optimization and decision problems involving multivariate polynomials are ubiquitous in many areas of engineering and applied mathematics. Although these problems can be approached using very general decision-theoretic methods (e.g., quantifier elimination, cylindrical algebraic decomposition, etc), in recent years there has been much interest in the use of convex optimization based symbolic-numeric techniques, at least for certain restricted class of problems. In this introductory talk we survey the basic features of these algebraic approaches, involving sum of squares (SOS) and semidefinite programming, emphasizing the geometric aspects and a few selected applications.
![]() Prof. Parrilo is the recipient of the 2005 Donald P. Eckman Award of the American Automatic Control Council, as well as the triennial SIAM Activity Group on Control and Systems Theory (SIAG/CST) Prize. He was also a finalist for the Tucker Prize of the Mathematical Programming Society for the years 2000-2003. He is currently in the Board of Directors of the Foundations of Computational Mathematics (FoCM) Society for the years 2000-2003. He is currently in the Board of Directors of the Foundations of Computational Mathematics (FoCM) society, an Associate Editor of the IEEE Transactions on Automatic Control, and a member of the Editorial Board of the MPS/SIAM Book Series on Optimization. His research interests include optimization methods for engineering applications, 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 engineering problems. Appointments: dcm@cs.cmu.edu |
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