An Introduction to Polynomial and Semi-Algebraic Optimization

By: Jean Bernard Lasserre

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Hardcover | 19 February 2015

At a Glance

Hardcover
354 Pages

Dimensions(cm)
22.86 x 15.24 x 2.06

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$251.48

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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.

Industry Reviews

'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 (R) 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
'This book provides an accessible introduction to very recent developments in the field of polynomial optimisation, i.e., the task of finding the infimum of a polynomial function on a set defined by polynomial constraints ... Every chapter contains additional exercises and a guide to the (free) Matlab software GloptiPoly. Therefore, this really well-written book provides an ideal introduction for individual learning and is well suited as the basis for a course on polynomical optimisation. Cordian Riener, Mathematical Reviews

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