Handbook on Semidefinite, Conic and Polynomial Optimization

1. Introduction to Semidefinite, Conic and Polynomial Optimization
Miguel F. Anjos, Jean B. Lasserre

2. The Approach of Moments for Polynomial Equations
Monique Laurent, Philipp Rostalski

3. Algebraic Degree in Semidefinite and Polynomial Optimization
Kristian Ranestad

4. Semidefinite Representation of Convex Sets and Convex Hulls
J. William Helton, Jiawang Nie

5. Convex Hulls of Algebraic Sets
João Gouveia, Rekha Thomas

6. Convex Relaxations and Integrality Gaps
Eden Chlamtac, Madhur Tulsiani

7. Relaxations of Combinatorial Problems Via Association Schemes
Etienne Klerk, Fernando M. Oliveira Filho, Dmitrii V. Pasechnik

8. Copositive Programming
Samuel Burer

9. Invariant Semidefinite Programs
Christine Bachoc, Dion C. Gijswijt, Alexander Schrijver, Frank Vallentin

10. A “Joint+Marginal” Approach in Optimization
Jean B. Lasserre

11. An Introduction to Formally Real Jordan Algebras and Their Applications in Optimization
F. Alizadeh

12. Complementarity Problems Over Symmetric Cones: A Survey of Recent Developments in Several Aspects
Akiko Yoshise

13. Convexity and Semidefinite Programming in Dimension-Free Matrix Unknowns
J. William Helton, Igor Klep, Scott McCullough

14. Positivity and Optimization: Beyond Polynomials
Jean B. Lasserre, Mihai Putinar

15. Self-Regular Interior-Point Methods for Semidefinite Optimization
Maziar Salahi, Tamás Terlaky

16. Elementary Optimality Conditions for Nonlinear SDPs
Florian Jarre

17. Recent Progress in Interior-Point Methods: Cutting-Plane Algorithms and Warm Starts
Alexander Engau

18. Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems
Sunyoung Kim, Masakazu Kojima

19. Block Coordinate Descent Methods for Semidefinite Programming
Zaiwen Wen, Donald Goldfarb, Katya Scheinberg

20. Projection Methods in Conic Optimization
Didier Henrion, Jérôme Malick

21. SDP Relaxations for Non-Commutative Polynomial Optimization
Miguel Navascués, Stefano Pironio, Antonio Acín

22. Semidefinite Programming and Constraint Programming
Willem-Jan Hoeve

23. The State-of-the-Art in Conic Optimization Software
Hans D. Mittelmann

24. Latest Developments in the SDPA Family for Solving Large-Scale SDPs
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata

25. On the Implementation and Usage of SDPT3 – A Matlab Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0
Kim-Chuan Toh, Michael J. Todd, Reha H. Tütüncü

26. PENNON: Software for Linear and Nonlinear Matrix Inequalities
Michal Kocvara, Michael Stingl

27. SDP Relaxations for Some Combinatorial Optimization Problems
Renata Sotirov

28. Computational Approaches to Max-Cut
Laura Palagi, Veronica Piccialli, Franz Rendl, Giovanni Rinaldi, Angelika Wiegele

29. Global Approaches for Facility Layout and VLSI Floorplanning
Miguel F. Anjos, Frauke Liers

30. Euclidean Distance Matrices and Applications
Nathan Krislock, Henry Wolkowicz

31. Sparse PCA: Convex Relaxations, Algorithms and Applications
Youwei Zhang, Alexandre d’Aspremont, Laurent El Ghaoui

Keywords: Economics/Management Science, Operations Research/Decision Theory, Operations Research, Management Science, Optimization