Introduction

In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems.

Classifications and Conditions

Classes of generic problems are defined in a simple and elegant manner by using only the two basic Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.

Focus of Explanations

Explanations focus on critical points and tangencies of polynomial optimization, Hölderian error bounds for polynomial systems, Frank-Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization.

Target Audience

It then goes on to look at optimization for the different types of polynomials. Through this text, graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.