[Review of the book An Introduction to Polynomial and Semi-Algebraic Optimization, Jean-Bernard Lasserre, 2015]

It is no exaggeration to say that Jean-Bernard Lasserre has revolutionized the field of polynomial global optimization in the last 15 years. He was awarded the Lagrange Prize for the first, seminal paper (Lasserre, 2001) where his new semidefinite programming-based approach was introduced, and most recently the INFORMS Optimization Society Khachiyan Prize for his collected works. As the title suggests, this new book by Lasserre is aimed at a fairly general audience, and it is remarkable to note that almost all the content dates from this century. There is some overlap with the author's earlier book (Lasserre, 2010), but the new volume has a narrower scope and is written at a more introductory level. For example, the new book includes exercises and a software (Gloptipoly) guide, and as such is suitable for a graduate course on polynomial optimization.