This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimizationAtheoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problemsAand rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization booksAfor example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the FermatAWeber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLABA toolbox CVX and a package of m-files that is posted on the bookAs web site.Chapter 1 For a comprehensive treatment of multidimensional calculus and linear algebra, the reader can refer to [24, 29, 33, 34, 35] and also Appendix A of [ 9]. Chapter 2 The topic of optimality conditions in Sections 2.1a2.3 is classical and can also be found in many other ... Chapter 5 More details and further extensions of Newtona#39;s method can be found, for example, in [9, 15, ... Chapter 8 A large variety of examples of convex optimization problems can be found in [13] and also in [8].

Title | : | Introduction to Nonlinear Optimization |

Author | : | Amir Beck |

Publisher | : | SIAM - 2014-10-27 |

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