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Real Algebraic Geometry and Optimization
 
Thorsten Theobald Goethe University Frankfurt, Frankfurt am Main, Germany
Hardcover ISBN:  978-1-4704-7431-7
Product Code:  GSM/241
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-1-4704-7636-6
Product Code:  GSM/241.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7635-9
Product Code:  GSM/241.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7636-6
eBook: ISBN:  978-1-4704-7635-9
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
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Real Algebraic Geometry and Optimization
Thorsten Theobald Goethe University Frankfurt, Frankfurt am Main, Germany
Hardcover ISBN:  978-1-4704-7431-7
Product Code:  GSM/241
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-1-4704-7636-6
Product Code:  GSM/241.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7635-9
Product Code:  GSM/241.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7636-6
eBook ISBN:  978-1-4704-7635-9
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 Details
     
     
    Graduate Studies in Mathematics
    Volume: 2412024; 293 pp
    MSC: Primary 14; 90; 68; 12; 52

    This book provides a comprehensive and user-friendly 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.

    Readership

    Undergraduate 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 Tarski-Sidenberg 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
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 2412024; 293 pp
MSC: Primary 14; 90; 68; 12; 52

This book provides a comprehensive and user-friendly 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.

Readership

Undergraduate and graduate students interested in real algebraic geometry and polynomial and semidefinite optimization.

  • Foundations
  • Univariate real polynomials
  • From polyhedra to semialgebraic sets
  • The Tarski-Sidenberg 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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