Moment and Polynomial Optimization

Overview of the book

Moment and polynomial optimization is an active research field. It is used to solve difficult questions in many areas, including global optimization, tensor computation, saddle points, Nash equilibrium, and bilevel programs. This book synthesizes current research and applications to provide the reader with
  • a systematic introduction to theory and methods,
  • a comprehensive approach for extracting optimizers and solving truncated moment problems, and
  • a creative methodology for using optimality conditions to construct tight Moment-SOS relaxations.

    • Intended Audience

    This book gives a quick, efficient introduction to the field of moment and polynomial optimization. It gives an accurate and concise introduction to optimality certificates, nonnegativity certificates for polynomials, Moment-SOS hierarchies, finite convergence theory, tight relaxtions, characterization of moments, representations for convex sets, and various Positivstellensatz. The book is especially suitable for graduate students, junior scholars, applied mathematicians, engineers and researchers to enter the field. It can also be used as a textbook for graduate students or as a monograph for scholars working in relevant fields.

    Publication Information

  • Title: Moment and Polynomial Optimization
  • Author: Jiawang Nie
  • Publisher: Society for Industrial and Applied Mathematics, 2023
  • Series: MOS-SIAM series on optimization (MO31)
  • ISBN: 978-1-61197-759-2
  • eISBN:978-1-61197-760-8
  • Availability: The book can be bought in SIAM book store .
  • To get a free electornic copy, send an email request to the author: njw AT math DOT ucsd DOT edu.

    • Table of Contents

  • Chapter 1: Basics of Linear Convex Optimization
  • Chapter 2: Introductions to Algebra, Polynomials, and Moments
  • Chapter 3: Univariate Nonnegative Polynomials and Moments
  • Chapter 4: Unconstrained Polynomial Optimization
  • Chapter 5: Constrained Polynomial Optimization
  • Chapter 6: Tight Moment-SOS Hierarchies
  • Chapter 7: Convexity with Polynomials and Sets
  • Chapter 8: Conic Optimization with Moments and Polynomials
  • Chapter 9: Copositive and CP Optimization
  • Chapter 10: Matrix Polynomials, Moments, and Optimization
  • Chapter 11: Tensor Optimization
  • Chapter 12: Special Topics

    • Erratum

    If a reader finds any kind of mistakes for the book, please send email to the author directly. Thanks a lot in advance!