Introduction to Nonlinear Optimization Theory, Algorithms, and Applications with MATLAB
By: Amir Beck (author)Paperback
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The three pillars of optimization theory - theoretical and algorithmic foundation, familiarity with applications, and the ability to apply theory and algorithms to actual problems - are combined in this book, which rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 exercises that deepen and enhance the reader's understanding of the topics. The author includes several subjects not typically found in optimization books, including optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. It also offers a large number of applications, such as circle fitting, the Fermat-Weber problem, denoising, clustering, and orthogonal regression. Theoretical and algorithmic topics are demonstrated by the MATLAB toolbox CVX and a package of m-files posted on the book's website. This book is intended for students of mathematics, computer science, and engineering at the advanced undergraduate level plus.
Amir Beck is an Associate Professor in the Department of Industrial Engineering at the Technion - Israel Institute of Technology. He has published numerous papers, has given invited lectures at international conferences, and was awarded the Salomon Simon Mani Award for Excellence in Teaching and the Henry Taub Research Prize. He is on the editorial board of Mathematics of Operations Research, Operations Research, and the Journal of Optimization Theory and Applications.
Preface; 1. Mathematical preliminaries; 2. Optimality conditions for unconstrained optimization; 3. Least squares; 4. The gradient method; 5. Newton's method; 6. Convex sets; 7. Convex functions; 8. Convex optimization; 9. Optimization over a convex set; 10. Optimality conditions for linearly constrained problems; 11. The KKT conditions; 12. Duality; Bibliographic notes; Bibliography; Index.
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- ID: 9781611973648
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