Semidefinite Optimization and Convex Algebraic Geometry

Grigoriy Blekherman is an assistant professor at Georgia Institute of Technology and a 2012 recipient of the Sloan Research Fellowship. His research interests lie at the intersection of convex and algebraic geometry. Pablo A. Parrilo is a Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. He has received the SIAG/CST Prize and the IEEE Antonio Ruberti Young Researcher Prize. His research interests include mathematical optimization, systems and control theory, and computational methods for engineering applications. Rekha R. Thomas is a Professor of Mathematics at the University of Washington. Her research interests are in optimization and computational algebra.

List of contributors; List of figures; Preface; List of notation; 1. What is convex algebraic geometry? Grigoriy Blekherman, Pablo A. Parrilo and Rekha R. Thomas; 2. Semidefinite optimization Pablo A. Parrilo; 3. Polynomial optimization, sums of squares, and applications Pablo A. Parrilo; 4. Nonnegative polynomials and sums of squares Grigoriy Blekherman; 5. Dualities Philipp Rostalski and Bernd Sturmfels; 6. Semidefinite representability Jiawang Nie; 7. Convex hulls of algebraic sets Joao Gouveia and Rekha R. Thomas; 8. Free convexity J. William Helton, Igor Klep and Scott McCullough; 9. Sums of Hermitian squares: old and new Mihai Putinar; Appendix A. Background material Grigoriy Blekherman, Pablo A. Parrilo and Rekha R. Thomas; Index.