This booklet offers a self-contained, obtainable creation to the mathematical advances and demanding situations because of using semidefinite programming in polynomial optimization. This speedy evolving study sector with contributions from the various fields of convex geometry, algebraic geometry, and optimization is named convex algebraic geometry.
each one bankruptcy addresses a basic point of convex algebraic geometry. The e-book starts with an advent 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 examine. those contain semidefinite representability of convex units, duality conception from the perspective of algebraic geometry, and nontraditional subject matters resembling sums of squares of advanced types and noncommutative sums of squares polynomials.
appropriate for a category or seminar, with routines aimed toward educating the subjects to novices, Semidefinite Optimization and Convex Algebraic Geometry serves as some extent of access into the topic for readers from a number of groups corresponding to engineering, arithmetic, and laptop technology. A consultant to the required heritage fabric comes in the appendix.
Audience This publication can function a textbook for graduate-level classes providing the elemental arithmetic at the back of convex algebraic geometry and semidefinite optimization. Readers undertaking study in those components will notice open difficulties and capability examine 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7: Convex Hulls of Algebraic units; bankruptcy eight: loose Convexity; bankruptcy nine: Sums of Hermitian Squares: outdated and New; Appendix A: historical past Material.
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