Positivity Certificates Polynomial Optimization
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Certificates Of Positivity For Real Polynomials
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Author : Victoria Powers
language : en
Publisher: Springer Nature
Release Date : 2021-11-26
Certificates Of Positivity For Real Polynomials written by Victoria Powers and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-26 with Mathematics categories.
This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of positivity for a real polynomial is an algebraic identity that gives an immediate proof of a positivity condition for the polynomial. Certificates of positivity have their roots in fundamental work of David Hilbert from the late 19th century on positive polynomials and sums of squares. Because of the numerous applications of certificates of positivity in mathematics, applied mathematics, engineering, and other fields, it is desirable to have methods for finding, describing, and characterizing them. For many of the topics covered in this book, appropriate algorithms, computational methods, and applications are discussed. This volume contains a comprehensive, accessible, up-to-date treatment of certificates of positivity, written by an expert in the field. It provides an overview of both the theory and computational aspects of the subject, and includes many of the recent and exciting developments in the area. Background information is given so that beginning graduate students and researchers who are not specialists can learn about this fascinating subject. Furthermore, researchers who work on certificates of positivity or use them in applications will find this a useful reference for their work.
Positivity Certificates Polynomial Optimization
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Author : William H. Krill
language : en
Publisher:
Release Date : 2020
Positivity Certificates Polynomial Optimization written by William H. Krill and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Handbook On Semidefinite Conic And Polynomial Optimization
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Author : Miguel F. Anjos
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-19
Handbook On Semidefinite Conic And Polynomial Optimization written by Miguel F. Anjos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-19 with Business & Economics categories.
Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.
Polynomial Optimization Moments And Applications
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Author : Michal Kočvara
language : en
Publisher: Springer Nature
Release Date : 2023-12-27
Polynomial Optimization Moments And Applications written by Michal Kočvara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-27 with Mathematics categories.
Polynomial optimization is a fascinating field of study that has revolutionized the way we approach nonlinear problems described by polynomial constraints. The applications of this field range from production planning processes to transportation, energy consumption, and resource control. This introductory book explores the latest research developments in polynomial optimization, presenting the results of cutting-edge interdisciplinary work conducted by the European network POEMA. For the past four years, experts from various fields, including algebraists, geometers, computer scientists, and industrial actors, have collaborated in this network to create new methods that go beyond traditional paradigms of mathematical optimization. By exploiting new advances in algebra and convex geometry, these innovative approaches have resulted in significant scientific and technological advancements. This book aims to make these exciting developments accessible to a wider audienceby gathering high-quality chapters on these hot topics. Aimed at both aspiring and established researchers, as well as industry professionals, this book will be an invaluable resource for anyone interested in polynomial optimization and its potential for real-world applications.
An Introduction To Polynomial And Semi Algebraic Optimization
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Author : Jean Bernard Lasserre
language : en
Publisher: Cambridge University Press
Release Date : 2015-02-19
An Introduction To Polynomial And Semi Algebraic Optimization written by Jean Bernard Lasserre and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-19 with Mathematics categories.
The first comprehensive introduction to the powerful moment approach for solving global optimization problems.
Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes
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Author : Didier Henrion
language : en
Publisher: World Scientific
Release Date : 2020-11-04
Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes written by Didier Henrion and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-04 with Mathematics categories.
The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.
Facets Of Algebraic Geometry
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Author : Paolo Aluffi
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-07
Facets Of Algebraic Geometry written by Paolo Aluffi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-07 with Mathematics categories.
Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
Combinatorial Optimization
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Author : William Cook
language : en
Publisher: Wiley-Interscience
Release Date : 1997-11-26
Combinatorial Optimization written by William Cook and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-26 with Mathematics categories.
Combinatorial optimization is a topic in discrete mathematics and theoretical computer science. This book covers the theory, algorithms and applications in a manner which should be accessible to researchers and post graduate students in mathematics and computer science.
Lyapunov Based Analysis And Controller Synthesis For Polynomial Systems Using Sum Of Squares Optimization
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Author : Zachary William Jarvis-Wloszek
language : en
Publisher:
Release Date : 2003
Lyapunov Based Analysis And Controller Synthesis For Polynomial Systems Using Sum Of Squares Optimization written by Zachary William Jarvis-Wloszek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Nonlinear Optimization
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Author : Stephen A. Vavasis
language : en
Publisher: Oxford University Press, USA
Release Date : 1991
Nonlinear Optimization written by Stephen A. Vavasis and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Computers categories.
The fields of computer science and optimization greatly influence each other, and this book is about one important connection between the two: complexity theory. Complexity theory underlies computer algorithms and is used to address such questions as the efficiency of algorithms and the possibility of algorithmic solutions for particular problems. Furthermore, as optimization problems increase in size with hardware capacity, complexity theory plays a steadily growing role in the exploration of optimization algorithms. As larger and more complicated problems are addressed, it is more important than ever to understand the asymptotic complexity issues. This book describes some of the key developments in the complexity aspects of optimization during the last decade. It will be a valuable source of information for computer scientists and computational mathematicians.