Approximation Methods for Polynomial Optimization: Models, Algorithms, and Applications

by Zhening Li, Simai He, Shuzhong Zhang

Overview

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.

Product Details

ISBN-13:	9781461439837
Publisher:	Springer New York
Publication date:	07/24/2012
Series:	SpringerBriefs in Optimization
Edition description:	2012
Pages:	124
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

1. ​Introduction.-2. Polynomial over the Euclidean Ball.- 3. Extensions of the Constraint Sets.- 4. Applications.- 5. Concluding Remarks.

Editorial Reviews

From the reviews:

“The book is an outgrowth of the first author’s Ph.D. thesis, defended in 2011 … . It is a well-written timely collection of state-of-the-art approximation algorithms for polynomial optimization problems … . All of the approximation results of the book are conveniently summarized and listed in table 5.1 for quick reference, with a unified nomenclature introduced in sections 1.3.1 and 1.3.2.” (Didier Henrion, Mathematical Reviews, March, 2013)

From the Publisher