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Genericity In Polynomial Optimization

2016-12-22 Mathematics
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Release : 2016-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 235/5 ( reviews)

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Book Synopsis Genericity In Polynomial Optimization by : Tien Son Pham

Download or read book Genericity In Polynomial Optimization written by Tien Son Pham. This book was released on 2016-12-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Genericity in Polynomial Optimization

2017 MATHEMATICS
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Release : 2017
Genre : MATHEMATICS
Kind : eBook
Book Rating : 225/5 ( reviews)

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Book Synopsis Genericity in Polynomial Optimization by : Huy-Vui Hà

Download or read book Genericity in Polynomial Optimization written by Huy-Vui Hà. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt:

Polynomial Optimization, Moments, and Applications

2024-01-28 Mathematics
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Release : 2024-01-28
Genre : Mathematics
Kind : eBook
Book Rating : 590/5 ( reviews)

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Book Synopsis Polynomial Optimization, Moments, and Applications by : Michal Kočvara

Download or read book Polynomial Optimization, Moments, and Applications written by Michal Kočvara. This book was released on 2024-01-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sparse Polynomial Optimization: Theory And Practice

2023-04-25 Mathematics
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Release : 2023-04-25
Genre : Mathematics
Kind : eBook
Book Rating : 966/5 ( reviews)

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Book Synopsis Sparse Polynomial Optimization: Theory And Practice by : Victor Magron

Download or read book Sparse Polynomial Optimization: Theory And Practice written by Victor Magron. This book was released on 2023-04-25. Available in PDF, EPUB and Kindle. Book excerpt: Many applications, including computer vision, computer arithmetic, deep learning, entanglement in quantum information, graph theory and energy networks, can be successfully tackled within the framework of polynomial optimization, an emerging field with growing research efforts in the last two decades. One key advantage of these techniques is their ability to model a wide range of problems using optimization formulations. Polynomial optimization heavily relies on the moment-sums of squares (moment-SOS) approach proposed by Lasserre, which provides certificates for positive polynomials. On the practical side, however, there is 'no free lunch' and such optimization methods usually encompass severe scalability issues. Fortunately, for many applications, including the ones formerly mentioned, we can look at the problem in the eyes and exploit the inherent data structure arising from the cost and constraints describing the problem.This book presents several research efforts to resolve this scientific challenge with important computational implications. It provides the development of alternative optimization schemes that scale well in terms of computational complexity, at least in some identified class of problems. It also features a unified modeling framework to handle a wide range of applications involving both commutative and noncommutative variables, and to solve concretely large-scale instances. Readers will find a practical section dedicated to the use of available open-source software libraries.This interdisciplinary monograph is essential reading for students, researchers and professionals interested in solving optimization problems with polynomial input data.

Approximation Methods for Polynomial Optimization

2012-07-25 Mathematics
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Release : 2012-07-25
Genre : Mathematics
Kind : eBook
Book Rating : 841/5 ( reviews)

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Book Synopsis Approximation Methods for Polynomial Optimization by : Zhening Li

Download or read book Approximation Methods for Polynomial Optimization written by Zhening Li. This book was released on 2012-07-25. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications. This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science.

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