Handbook on semidefinite, conic and polynomial optimization / Miguel F. Anjos, Jean B. Lasserre ; editors.

Format:

Book

Contributor:

Anjos, Miguel F.

Lasserre, Jean-Bernard, 1953-

Series:

International series in operations research & management science ; v. 166.

International series in operations research & management science ; v. 166

Language:

English

Subjects (All):

Mathematical optimization--Research.

Mathematical optimization.

Linear programming.

Physical Description:

1 online resource (954 p.)

Edition:

1st ed. 2012.

Place of Publication:

New York : Springer, c2012.

Language Note:

English

Summary:

Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Contents:

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.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613443564

9781283443562

1283443562

9781461407690

1461407699

OCLC:

765367213