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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.

Polynomial Approximations for Infinite-dimensional Optimization Problems

2013
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Release : 2013
Genre :
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Book Synopsis Polynomial Approximations for Infinite-dimensional Optimization Problems by :

Download or read book Polynomial Approximations for Infinite-dimensional Optimization Problems written by . This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation Theory and Methods

1981-03-31 Mathematics
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Release : 1981-03-31
Genre : Mathematics
Kind : eBook
Book Rating : 147/5 ( reviews)

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Book Synopsis Approximation Theory and Methods by : M. J. D. Powell

Download or read book Approximation Theory and Methods written by M. J. D. Powell. This book was released on 1981-03-31. Available in PDF, EPUB and Kindle. Book excerpt: Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.

Approximation Theory and Optimization

1997-11-13 Mathematics
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Release : 1997-11-13
Genre : Mathematics
Kind : eBook
Book Rating : 905/5 ( reviews)

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Book Synopsis Approximation Theory and Optimization by : M. D. Buhmann

Download or read book Approximation Theory and Optimization written by M. D. Buhmann. This book was released on 1997-11-13. Available in PDF, EPUB and Kindle. Book excerpt: Michael Powell is one of the world's foremost figures in numerical analysis. This volume, first published in 1997, is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell's own achievements, focuses on innovative work in optimisation and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys. They have all been reviewed and edited to form a coherent volume for this important discipline within mathematics, with highly relevant applications throughout science and engineering.

Sparse Polynomial Approximation of High-Dimensional Functions

2022-02-16 Mathematics
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Release : 2022-02-16
Genre : Mathematics
Kind : eBook
Book Rating : 88X/5 ( reviews)

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Book Synopsis Sparse Polynomial Approximation of High-Dimensional Functions by : Ben Adcock

Download or read book Sparse Polynomial Approximation of High-Dimensional Functions written by Ben Adcock . This book was released on 2022-02-16. Available in PDF, EPUB and Kindle. Book excerpt: Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

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