This updated new edition includes a wealth of additional material. As well as its integration of mathematical theory and numerical algorithm development, it features new chapters on topics such as the calculus of variations, integration, and block relaxation.

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students' skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications.In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.

Provides an integration of mathematical theory and development of numerical algorithms for applied optimization Includes new chapters on calculus of variations, integration, and block relaxation Showcases balance between presentation of mathematical theory and development of numerical algorithms Includes supplementary material: sn.pub/extras

Autorentext

Kenneth Lange is the Rosenfeld Professor of Computational Genetics in the Departments of Computational Medicine, Human Genetics, and Statistics at the University of California, Los Angeles. He served as chair of the UCLA Department of Computational Medicine for 9 years and as chair of the UCLA Department of Human Genetics for 12 years. He has authored five other books, including Mathematical and Statistical Methods for Genetic Analysis (Springer, 2002), Numerical Analysis for Statisticians (Springer, 2010) and Optimization (Springer, 2013). In 2021 he was elected to the National Academy of Sciences.

Zusammenfassung
The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications.In this second edition the emphasis remains on finite-dimensional optimization.

Inhalt

Elementary Optimization.- The Seven C's of Analysis.- The Gauge Integral.- Differentiation.- Karush-Kuhn-Tucker Theory.- Convexity.- Block Relaxation.- The MM Algorithm.- The EM Algorithm.- Newton's Method and Scoring.- Conjugate Gradient and Quasi-Newton.- Analysis of Convergence.- Penalty and Barrier Methods.- Convex Calculus.- Feasibility and Duality.- Convex Minimization Algorithms.- The Calculus of Variations.- Appendix: Mathematical Notes.- References.- Index.