Semidefinite Optimization and Convex Algebraic Geometry

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 João 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.