Polynomial Optimization, Moments, and Applications

This introductory book explores the latest research developments in polynomial optimization, presenting the results of cutting-edge interdisciplinary work conducted by the European network POEMA. For the past four years, experts from various fields, including algebraists, geometers, computer scientists, and industrial actors, have collaborated in this network to create new methods that go beyond traditional paradigms of mathematical optimization. By exploiting new advances in algebra and convex geometry, these innovative approaches have resulted in significant scientific and technological advancements. This book aims to make these exciting developments accessible to a wider audienceby gathering high-quality chapters on these hot topics.

Aimed at both aspiring and established researchers, as well as industry professionals, this book will be an invaluable resource for anyone interested in polynomial optimization and its potential for real-world applications.

Bernard Mourrain is research director at Inria of Université Côte d'Azur. He was at École Normale Supérieure de Cachan from 1984 to 1988, got his PhD at the center of Mathematics of École Polytechnique in 1991, his Habilitation à Diriger des Recherches at the University of Nice in 1997. His research interests include symbolic and numeric computation, polynomial systems solving, polynomial optimization, effective algebraic geometry, geometric modeling, isogeometric analysis.

Cordian Riener is a professor of mathematics at UiT The Arctic University of Norway, located in Tromsø, Norway. He studied mathematical economics, mathematics and philosophy at Ulm University, the University Bordeaux 2, and Goethe University Frankfurt. After completing his PhD in mathematics at Goethe University Frankfurt, he worked as a postdoc at the University of Konstanz and Aalto University. His interests are focused on mathematical structures in computation, optimization, and computational complexity.