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.
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