This accessible overview introduces the Christoffel-Darboux kernel as a novel, simple and efficient tool in statistical data analysis.

Polynomial optimization is a fascinating field of study that has revolutionized the way we approach nonlinear problems described by polynomial constraints. The applications of this field range from production planning processes to transportation, energy consumption, and resource control. 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 audience by 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.

This book presents a systematic and in-depth treatment of some basic topics in approximation theory in an effort to emphasize the rich connections of different branches of analysis with this subject. It contains a good blend of both the classical as well as abstract topics in the domain and their interconnections as appropriate. The approach is from the very concrete to more and more abstract levels. In order to provide a historical perspective on the results, a section on notes is appended to each chapter with an extensive bibliography. Researchers will find several references to recent developments. Problems of varying degree of difficulty accompany each chapter. Some of these problems complement certain results from the text. The others, more challenging, are drawn from the contemporary research articles. Ample hints are provided for such problems. Primarily aimed at graduate students and teachers of mathematics, researchers interested in an introduction to the specific results or techniques of approximation theory will find this book very attractive.

Contains research articles on the mathematics and applications of control theory and on those parts of optimization theory concerned with the dynamics of deterministic or stochastic systems in continuous or discrete time or otherwise dealing with differential equations, dynamics, infinite-dimensional spaces, or fundamental issues in variational analysis and geometry.