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Approximation Methods for Polynomial Optimization: Models, Algorithms, and Applications (SpringerBriefs in Optimization)

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Polynomial optimization, as its name suggests, is used to optimize a generic multivariate polynomial function, subject to some suitable polynomial equality and/or inequality constraints. Such problem formulation dates back to the nineteenth century when the relationship between nonnegative polynomials and sum of squares (SOS) was discussed by Hilbert. Polynomial optimization is one of the fundamental problems in Operations Research and has applications in a wide range of areas, including biomedical engineering, control theory, graph theory, investment science, material science, numerical linear algebra, quantum mechanics, signal processing, speech recognition, among many others. This brief discusses some important subclasses of polynomial optimization models arising from various applications. The focus is on optimizing a high degree polynomial function over some frequently encountered constraint sets, such as the Euclidean ball, the Euclidean sphere, intersection of co-centered ellipsoids, binary hypercube, general convex compact set, and possibly a combination of the above constraints. All the models under consideration are NP-hard in general. In particular, this brief presents a study on the design and analysis of polynomial-time approximation algorithms, with guaranteed worst-case performance ratios. We aim at deriving the worstcase performance/approximation ratios that are solely dependent on the problem dimensions, meaning that they are independent of any other types of the problem parameters or input data. The new techniques can be applied to solve even broader classes of polynomial/tensor optimization models. Given the wide applicability of the polynomial optimization models, the ability to solve such models—albeit approximately—is clearly beneficial. To illustrate how such benefits might be, we present a variety of examples in this brief so as to showcase the potential applications of polynomial optimization.
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Oracle Built in Packages
Oracle Built in Packages
Oracle is the most popular database management system in use today, and PL/SQL plays a pivotal role in current and projected Oracle products and applications. PL/SQL is a programming language providing procedural extensions to the SQL relational database language and to an ever-growing number of oracle development tools. originally a rather limited...
The Definitive Guide to Stellent Content Server Development
The Definitive Guide to Stellent Content Server Development

The Definitive Guide to Stellent Content Server Development is the most complete book available for this Enterprise Content Management application. It gives an introduction to Content Management, followed by an in-depth discussion of Stellent's core service-oriented architecture.

It details how its flexible, component-driven...

Building Apps for the Universal Windows Platform: Explore Windows 10 Native, IoT, HoloLens, and Xamarin
Building Apps for the Universal Windows Platform: Explore Windows 10 Native, IoT, HoloLens, and Xamarin

Develop Windows 10 applications faster and more efficiently using the Universal Windows Platform. You will use Xamarin to create apps for macOS, iOS, and Android devices.

Building Apps for the Universal Windows Platform is a complete guide covering PCs, tablets, phones, and other devices such as HoloLens. You...


Radar Cross Section, 2nd Edition (Scitech Radar and Defense)
Radar Cross Section, 2nd Edition (Scitech Radar and Defense)
This is the second edition of the first and foremost book on this subject for self-study, training, and course work. Radar cross section (RCS) is a comparison of two radar signal strengths. One is the strength of the radar beam sweeping over a target, the other is the strength of the reflected echo sensed by the receiver. This book shows how the...
Color Atlas of Dermatopathology (Dermatology: Clinical & Basic Science)
Color Atlas of Dermatopathology (Dermatology: Clinical & Basic Science)

This outstanding dermatopathology atlas emphasizes the correlation of pathological findings with clinical presentations and presents a reader-friendly approach to the diagnosis and interpretation of skin biopsy results. With an abundance of color clinical and histologic photographs, and descriptions of numerous dermatological diseases and...

A Photographic Atlas for the Microbiology Laboratory
A Photographic Atlas for the Microbiology Laboratory

This full-color atlas is intended to act as a supplement to introductory microbiology laboratory manuals. It is not designed to replace them, nor is it intended to replace actual performance of the techniques. Rather, the photographs are supplied to help with the interpretation of results.
The third edition of the Photographic Atlas
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