This publication offers a self-contained, available advent to the mathematical advances and demanding situations caused by using semidefinite programming in polynomial optimization. This quick evolving study quarter with contributions from the varied fields of convex geometry, algebraic geometry, and optimization is called convex algebraic geometry.
each one bankruptcy addresses a basic element of convex algebraic geometry. The booklet starts with an advent to nonnegative polynomials and sums of squares and their connections to semidefinite programming and quick advances to a number of components on the vanguard of present study. those contain semidefinite representability of convex units, duality idea from the perspective of algebraic geometry, and nontraditional subject matters corresponding to sums of squares of complicated kinds and noncommutative sums of squares polynomials.
compatible for a category or seminar, with workouts aimed toward educating the subjects to newcomers, Semidefinite Optimization and Convex Algebraic Geometry serves as some extent of access into the topic for readers from a number of groups akin to engineering, arithmetic, and computing device technological know-how. A advisor to the required heritage fabric comes in the appendix.
Audience This ebook can function a textbook for graduate-level classes offering the fundamental arithmetic at the back of convex algebraic geometry and semidefinite optimization. Readers accomplishing study in those parts will become aware of open difficulties and capability learn directions.
Contents: checklist of Notation; bankruptcy 1: what's Convex Algebraic Geometry?; bankruptcy 2: Semidefinite Optimization; bankruptcy three: Polynomial Optimization, Sums of Squares, and functions; bankruptcy four: Nonnegative Polynomials and Sums of Squares; bankruptcy five: Dualities; bankruptcy 6: Semidefinite Representability; bankruptcy 7: Convex Hulls of Algebraic units; bankruptcy eight: unfastened Convexity; bankruptcy nine: Sums of Hermitian Squares: outdated and New; Appendix A: historical past Material.
Read or Download Semidefinite Optimization and Convex Algebraic Geometry (MPS-SIAM Series on Optimization) PDF
Best Algebraic Geometry books
An obtainable textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the speculation of affine algebraic teams from first ideas. construction at the heritage fabric from algebraic geometry and algebraic teams, the textual content presents an creation to extra complex and specialized fabric.
The idea of elliptic curves is distinct by means of its lengthy background and by way of the variety of the tools which have been utilized in its learn. This e-book treats the mathematics technique in its glossy formula, by using simple algebraic quantity idea and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal team of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields.
This seriously class-tested publication is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A easy wisdom of algebra and topology on the first yr graduate point of an American college is believed. the 1st half is worried with hyperbolic geometry and discrete teams.
Additional info for Semidefinite Optimization and Convex Algebraic Geometry (MPS-SIAM Series on Optimization)