Genericity in Polynomial Optimization

Nonfiction, Science & Nature, Mathematics
Cover of the book Genericity in Polynomial Optimization by Huy-Vui Hà, Tiến-Sơn Phạm, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Huy-Vui Hà, Tiến-Sơn Phạm ISBN: 9781786342232
Publisher: World Scientific Publishing Company Publication: December 22, 2016
Imprint: WSPC (EUROPE) Language: English
Author: Huy-Vui Hà, Tiến-Sơn Phạm
ISBN: 9781786342232
Publisher: World Scientific Publishing Company
Publication: December 22, 2016
Imprint: WSPC (EUROPE)
Language: English

In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.

Explanations focus on critical points and tangencies of polynomial optimization, Hölderian error bounds for polynomial systems, Frank–Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.

Contents:

  • Semi-Algebraic Geometry
  • Critical Points and Tangencies
  • Hölderian Error Bounds for Polynomial Systems
  • Frank–Wolfe Type Theorem for Polynomial Programs
  • Well-Posedness in Unconstrained Polynomial Optimization
  • Generic Properties in Polynomial Optimization
  • Optimization of Polynomials on Compact Semi-Algebraic Sets
  • Optimization of Polynomials on Non-Compact Semi-Algebraic Sets
  • Convex Polynomial Optimization

Readership: Graduate students, PhD Students and researchers of mathematics.
Key Features:

  • The book will complement what is already rather extensively covered in the existing recent books, like the ones of Jean Bernard Lasserre, Monique Laurent, and Murray Marshall
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.

Explanations focus on critical points and tangencies of polynomial optimization, Hölderian error bounds for polynomial systems, Frank–Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.

Contents:

Readership: Graduate students, PhD Students and researchers of mathematics.
Key Features:

More books from World Scientific Publishing Company

Cover of the book George Placzek by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Ordinary Differential Equations with Applications by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book The Story of Genetics, Development and Evolution by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Context-Free Languages and Primitive Words by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Probability and Expectation by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Silver Shades of Grey by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Science: Image in Action by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book China by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book The Great Equal Society by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book International Seminar on Nuclear War and Planetary Emergencies — 45th Session by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Social Construction in Contemporary China by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Perspectives in Micro- and Nanotechnology for Biomedical Applications by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book The Kish Cypher by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Adventures in Cosmology by Huy-Vui Hà, Tiến-Sơn Phạm
Cover of the book Evidence-based Clinical Chinese Medicine by Huy-Vui Hà, Tiến-Sơn Phạm
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy