This e-book offers a self-contained, available advent to the mathematical advances and demanding situations due to using semidefinite programming in polynomial optimization. This quick evolving learn sector with contributions from the varied fields of convex geometry, algebraic geometry, and optimization is called convex algebraic geometry.

each one bankruptcy addresses a primary element of convex algebraic geometry. The ebook starts with an creation to nonnegative polynomials and sums of squares and their connections to semidefinite programming and speedy advances to a number of parts on the leading edge of present study. those contain semidefinite representability of convex units, duality conception from the perspective of algebraic geometry, and nontraditional subject matters comparable to sums of squares of advanced kinds and noncommutative sums of squares polynomials.

compatible for a category or seminar, with routines geared toward educating the subjects to rookies, Semidefinite Optimization and Convex Algebraic Geometry serves as some extent of access into the topic for readers from a number of groups equivalent to engineering, arithmetic, and machine technology. A advisor to the mandatory historical past fabric comes in the appendix.

Audience This e-book can function a textbook for graduate-level classes offering the elemental arithmetic at the back of convex algebraic geometry and semidefinite optimization. Readers engaging in examine in those components will realize open difficulties and capability learn directions.

Contents: record of Notation; bankruptcy 1: what's Convex Algebraic Geometry?; bankruptcy 2: Semidefinite Optimization; bankruptcy three: Polynomial Optimization, Sums of Squares, and purposes; bankruptcy four: Nonnegative Polynomials and Sums of Squares; bankruptcy five: Dualities; bankruptcy 6: Semidefinite Representability; bankruptcy 7: Convex Hulls of Algebraic units; bankruptcy eight: loose Convexity; bankruptcy nine: Sums of Hermitian Squares: previous and New; Appendix A: history Material.

Show description

Read or Download Semidefinite Optimization and Convex Algebraic Geometry (MPS-SIAM Series on Optimization) PDF

Similar Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly principles from algebraic topology, sensible research and geometry. it's a device - a method of conveying info between those 3 topics - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this publication is to acquaint the reader with the basic rules of analytic K-homology and boost a few of its functions.

The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)

First textbook-level account of simple examples and strategies during this quarter. appropriate for self-study by means of a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yankee Mathematical Society, in addition to a winning Springer writer.


"It offers a delicate portrait of an outstanding individual. It describes effectively and intelligibly on a nontechnical point the realm of mathematical rules during which Hilbert created his masterpieces. And it illuminates the heritage of German social heritage opposed to which the drama of Hilberts existence was once performed.

Introduction to Analysis of the Infinite: Book I

From the preface of the writer: ". .. i've got divided this paintings into books; within the first of those i've got restricted myself to these issues relating natural research. within the moment booklet i've got defined these factor which has to be identified from geometry, considering that research is quite often built in the sort of manner that its software to geometry is proven.

Extra info for Semidefinite Optimization and Convex Algebraic Geometry (MPS-SIAM Series on Optimization)

Show sample text content

Rated 4.01 of 5 – based on 36 votes