ENGLISH

An Introduction to Polynomial and Semi-Algebraic Optimization

By Jean Bernard Lasserre

Book information

Publisher
Cambridge University Press
Year
2015
ISBN
978-1-107-06057-9
DOI
10.1017/CBO9781107447226
Language
english
Format
PDF
Filesize
3 MB (3386140 bytes)
Series
Cambridge Texts in Applied Mathematics № 52
Pages
354\354
Time added
2017-06-23 09:42:56
Polynomial optimization; Semi-Algebraic optimizati

Description

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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