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Jean Bernard Lasserre - An Introduction to Polynomial and Semi-Algebraic Optimization, Inbunden

Inbunden, Engelska, 2015

Del 52 i serien Cambridge Texts in Applied Mathematics

An Introduction to Polynomial and Semi-Algebraic Optimization

Av Jean Bernard Lasserre

2989 kr

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Beskrivning
This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.
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Jean Bernard Lasserre is Directeur de Recherche at the LAAS laboratory in Toulouse and a member of the Institute of Mathematics of Toulouse (IMT). In 2009 he received the Lagrange Prize, awarded jointly by the Mathematical Optimization Society (MOS) and the Society for Industrial and Applied Mathematics (SIAM). He is the winner of the 2015 INFORMS Optimization Society Khachiyan Prize, awarded for life-time achievements in the area of optimization.

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'This monograph may be considered as a comprehensive introduction to solving global optimization problems described by polynomials and even semi-algebraic functions. The book is accompanied by a MATLAB® freeware software that implements the described methodology … The well written and extensive introduction may help the reader to knowingly use the book.' Jerzy Ombach, Zentralblatt MATH

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