An Introduction to Polynomial and Semi-Algebraic Optimization
Jean Bernard Lasserre, Centre National de la Recherche Scientifique
Cambridge University Press, 2015
ISBN: 978-1-107-63069-7;
Language: English
An Introduction to Polynomial and Semi-Algebraic Optimization provides a 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.
Among other things, powerful positivity certificates from real algebraic geometry allow readers 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 An Introduction to Polynomial and Semi-Algebraic Optimization to understand, experiment with, and master this new approach through the simple worked examples provided.
MATLAB is used to solve examples in the book.
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