Handbook on Semidefinite, Conic and Polynomial Optimization

• Introduction to Semidefinite, Conic and Polynomial Optimization.- The Approach of Moments for Polynomial Equations.- Algebraic Degree in Semidefinite and Polynomial Optimization.- Semidefinite Representation of Convex Sets and Convex Hulls.- Convex Hulls of Algebraic Sets.- Convex Relations and Integrality Gaps.- Relaxations of Combinatorial Problems via Association Schemes.- Copositive Programming.- Invariant Semidefinite Programs.- A "Joint+Marginal" Approach in Optimization.- An Introduction to Formally Real Jordan Algebras and Their Applications in Optimization.- Complementarity Problems Over Symmetric Conics: A Survey of Recent Developments in Several Aspects.- Convexity and Semidefinite Programming in Dimension-Free Matrix Unknowns.- Positivity and Optimization: Beyond Polynomials.- Self-Regular Interior-Point Methods for Semidefinite Optimization.- Elementary Optimality Conditions for Nonlinear SDPs.- Recent Progress in Interior-Point Methods: Cutting Plane Algorithms and Warm Starts.- Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems.- Block Coordinate Descent Methods for Semidefinite Programming.- Projection Methods in Conic Optimization.- SDP Relaxations for Non-Commutative Polynomial Optimization.- Semidefinite Programming and Constraint Programming.- The State-of-the-Art in Conic Optimization Software.- Latest Developments in SDPA Family for Solving Large-Scale SDPs.- On the Implementation and Usage of SDPT3: A MATLAB Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0.- PENNON: Software for Linear and Nonlinear Matrix Inequalities.- SDP Relaxations for Some Combinatorial Optimization Problems.- Computational Approaches to Max-Cut.- Global Approaches for Facility Layout and VLSI Floorplanning.- Euclidean Distance Matrices and Applications.- Sparse PCA: Convex Relaxations, Algorithms and Applications.

From the reviews:“This volume is a collection of self contained survey papers on various aspects of semidefinite programming and polynomial optimization. The volume is divided into four sections, covering the theory of conic and polynomial optimization, algorithms, software implementations, and applications of semidefinite and polynomial optimization. … This is an advanced book and particularly in the theory section … . The papers in this volume will be of interest to advanced graduate students and researchers working in conic optimization, SDP, and polynomial optimization.” (Brian Borchers, The Mathematical Association of America, June, 2012)