Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB, Second Edition

Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author’s objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples.

Amir Beck is a professor at the School of Mathematical Sciences, Tel-Aviv University. His research interests are in continuous optimization, including theory, algorithmic analysis, and applications. He has published numerous papers and has given invited lectures at international conferences. He was awarded the INFORMS Farkas Prize (2022), the Salomon Simon Mani award for excellence in teaching, and the Henry Taub research prize. He serves on the editorial board of several journals. His research has been supported by various funding agencies, including the Israel Science Foundation, the German-Israeli Foundation, the Binational US-Israel foundation, the Israeli Science and Energy Ministries, and the European Community.