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Genericity In Polynomial Optimization af Tien Son Pham, Ha Huy Vui

Genericity In Polynomial Optimization (Series on Optimization and Its Applications)

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Beskrivelse: In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments... Læs mere

In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains rece... Læs mere

Produktdetaljer:

Sprog:
Engelsk
ISBN-13:
9781786342225
Sideantal:
260
Udgivet:
22-12-2016
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Forlagets beskrivelse
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, Holderian 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.

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