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Softcover ISBN:  9781470476366 
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eBook ISBN:  9781470476359 
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AMS Member Price:  $68.00 
Softcover ISBN:  9781470476366 
eBook: ISBN:  9781470476359 
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Hardcover ISBN:  9781470474317 
Product Code:  GSM/241 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9781470476366 
Product Code:  GSM/241.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470476359 
Product Code:  GSM/241.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470476366 
eBook ISBN:  9781470476359 
Product Code:  GSM/241.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 241; 2024; 293 ppMSC: Primary 14; 90; 68; 12; 52
This book provides a comprehensive and userfriendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications.
Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.
ReadershipUndergraduate and graduate students interested in real algebraic geometry and polynomial and semidefinite optimization.

Table of Contents

Foundations

Univariate real polynomials

From polyhedra to semialgebraic sets

The TarskiSidenberg principle and elimination of quantifiers

Cylindrical algebraic decomposition

Linear, semidefinite, and conic optimization

Positive polynomials, sums of suares and convexity

Positive polynomials

Polynomial optimization

Spectrahedra

Outlook

Stable and hyperbolic polynomials

Relative entropy methods in semialgebraic optimzation

Background material


Additional Material

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This book provides a comprehensive and userfriendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications.
Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.
Undergraduate and graduate students interested in real algebraic geometry and polynomial and semidefinite optimization.

Foundations

Univariate real polynomials

From polyhedra to semialgebraic sets

The TarskiSidenberg principle and elimination of quantifiers

Cylindrical algebraic decomposition

Linear, semidefinite, and conic optimization

Positive polynomials, sums of suares and convexity

Positive polynomials

Polynomial optimization

Spectrahedra

Outlook

Stable and hyperbolic polynomials

Relative entropy methods in semialgebraic optimzation

Background material