Handbook on Semidefinite, Conic and Polynomial Optimization

Abstract

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.