Author: Markus SchweighoferPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Certificates for Nonnegativity of Polynomials with Zeros on Compact Semialgebraic Sets
Certificates of Positivity for Real Polynomials
Author: Victoria PowersPublisher: Springer Nature
ISBN: 3030855473
Category : Mathematics
Languages : en
Pages : 161
Book Description
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.
Polynomial Optimization, Moments, and Applications
Author: Michal KočvaraPublisher: Springer Nature
ISBN: 3031386590
Category : Mathematics
Languages : en
Pages : 274
Book Description
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 audience by 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.
Non-negative Polynomials on Compact Semi-algebraic Sets in One Variable Case
Author: An Introduction to Polynomial and Semi-Algebraic Optimization
Author: Jean Bernard LasserrePublisher: Cambridge University Press
ISBN: 1107060575
Category : Mathematics
Languages : en
Pages : 355
Book Description
The first comprehensive introduction to the powerful moment approach for solving global optimization problems.
Genericity In Polynomial Optimization
Author: Tien Son PhamPublisher: World Scientific
ISBN: 1786342235
Category : Mathematics
Languages : en
Pages : 261
Book Description
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.
Semidefinite Optimization and Convex Algebraic Geometry
Author: Grigoriy BlekhermanPublisher: SIAM
ISBN: 1611972280
Category : Mathematics
Languages : en
Pages : 487
Book Description
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Global Optimization of Polynomial Functions and Applications
Author: Jiawang NiePositive Polynomials in Control
Author: Didier HenrionPublisher: Springer Science & Business Media
ISBN: 9783540239482
Category : Technology & Engineering
Languages : en
Pages : 332
Book Description
Positive Polynomials in Control originates from an invited session presented at the IEEE CDC 2003 and gives a comprehensive overview of existing results in this quickly emerging area. This carefully edited book collects important contributions from several fields of control, optimization, and mathematics, in order to show different views and approaches of polynomial positivity. The book is organized in three parts, reflecting the current trends in the area: 1. applications of positive polynomials and LMI optimization to solve various control problems, 2. a mathematical overview of different algebraic techniques used to cope with polynomial positivity, 3. numerical aspects of positivity of polynomials, and recently developed software tools which can be employed to solve the problems discussed in the book.
Integer Programming and Combinatorial Optimization
Author: Friedrich EisenbrandPublisher: Springer
ISBN: 3319592505
Category : Computers
Languages : en
Pages : 467
Book Description
This book constitutes the refereed proceedings of the 19th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2017, held in Waterloo, IN, Canada, in June 2017. The 36 full papers presented were carefully reviewed and selected from 125 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.