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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Semidefinite Optimization and Convex Algebraic Geometry (Paperback)
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Semidefinite Optimization and Convex Algebraic Geometry (Paperback)
Series: MOS-SIAM Series on Optimization, 13
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This book provides a self-contained, accessible introduction to the
mathematical advances and challenges resulting from the use of
semidefinite programming in polynomial optimization. This important
and highly applicable research area with contributions from convex
geometry, algebraic geometry, and optimization is known as convex
algebraic geometry. Each chapter addresses a fundamental aspect of
the topic, beginning with an introduction to nonnegative
polynomials and sums of squares, and their connections to
semidefinite programming. The material quickly advances to areas at
the forefront of current research, including semidefinite
representability of convex sets, duality theory in algebraic
geometry, and nontraditional topics such as sums of squares of
complex forms. The book is a suitable entry point to the subject
for readers at the graduate level or above in mathematics,
engineering or computer science. Instructors will find the book
appropriate for a class or seminar, and researchers will encounter
open problems and new research directions.
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