Semidefinite optimization and convex algebraic geometry / edited by Grigoriy Blekherman, Pablo A. Parrilo, Rekha R. Thomas.

Format:

Book

Contributor:

Blekherman, Grigoriy.

Parrilo, Pablo A.

Thomas, Rekha R., 1967-

Society for Industrial and Applied Mathematics.

Series:

MOS-SIAM series on optimization.

MOS-SIAM series on optimization

Language:

English

Subjects (All):

Semidefinite programming.

Convex geometry.

Geometry, Algebraic.

Physical Description:

1 electronic text (xix, 471 p.) : digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2012.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This quickly evolving research area with contributions from the diverse fields of convex geometry, algebraic geometry, and optimization is known as convex algebraic geometry. Each chapter addresses a fundamental aspect of convex algebraic geometry. The book begins with an introduction to nonnegative polynomials and sums of squares and their connections to semidefinite programming and quickly advances to several areas at the forefront of current research. These include semidefinite representability of convex sets, duality theory from the point of view of algebraic geometry, and nontraditional topics such as sums of squares of complex forms and noncommutative sums of squares polynomials.

Contents:

1. What is convex algebraic geometry?

2. Semidefinite optimization

3. Polynomial optimization, sums of squares, and applications

4. Nonnegative polynomials and sums of squares

5. Dualities

6. Semidefinite representability

7. Convex hulls of algebraic sets

8. Free convexity

9. Sums of Hermitian squares. Old and new

Appendix A. Background material

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Title from title screen, viewed 11/28/2012.

ISBN:

9781611972290 (electronic bk.)

1611972280

OCLC:

819588674

Publisher Number:

MO13 SIAM