Polynomial Optimization, Moments, and Applications

ISBN-13: 9783031386589 / Angielski

Michal Kočvara; Bernard Mourrain; Cordian Riener

Spis treści

1. Polynomial Optimization, Certificates of Positivity, and Christoffel Function.- 2. Relative entropy methods in constrained polynomial and signomial optimization.- 3. Symmetries in polynomial optimization.- 4. Copositive matrices, sums of squares and the stability number of a graph.- 5. Matrix factorization ranks via polynomial optimization.- 6. Polynomial optimization in geometric modeling.- 7. Assessing Safety for Control Systems Using Sum-of-Squares Programming.- 8. Polynomial Equations: Theory and Practice.

O autorze

Michal Kočvara is Professor in Mathematical Optimization at the University of Birmingham, UK, and a senior researcher at the Academy of Sciences of the Czech Republic. He (co-)authored a monograph and over 50 journal articles on various aspects of mathematical optimization and optimization of mechanical structures. He co-developed several computer programs for nonlinear and semidefinite optimization and optimization of elastic structures. His work has been supported by several EU grants.

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.

Blurb

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.