Semidefinite Optimization and Convex Algebraic Geometry (Mos-siam Series on Optimization)

Blekherman, Grigoriy (EDT)/ Parrilo, Pablo A. (EDT)/ Thomas, Rekha R.

Society for Industrial & Applied（2013/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 476 p.
• 言語 ENG
• 商品コード 9781611972283
• DDC分類 516.35

Full Description

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.* Nontraditional topics such as sums of squares of complex forms and noncommutative sums of squares polynomials.

Contents

* List of Notation* Chapter 1Chapter 2: Semidefinite Optimization* Chapter 3: Polynomial Optimization, Sums of Squares, and Applications* Chapter 4: Nonnegative Polynomials and Sums of Squares* Chapter 5: Dualities* Chapter 6: Semidefinite Representability* Chapter 7: Convex Hulls of Algebraic Sets* Chapter 8: Free Convexity* Chapter 9: Sums of Hermitian Squares: Old and New* Appendix A: Background Material