Optimization (Springer Texts in Statistics)

Description

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 convexity serves as bridge between linear and nonlinear programming and makes it possible to give a modern exposition of linear programming based on the interior point method rather than the simplex method.

The emphasis on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes graduate students in applied mathematics, computational biology, computer science, economics, and physics as well as upper division undergraduate majors in mathematics who want to see rigorous mathematics combined with real applications.

Chapter 1 reviews classical methods for the exact solution of optimization problems. Chapters 2 and 3 summarize relevant concepts from mathematical analysis. Chapter 4 presents the Karush-Kuhn-Tucker conditions for optimal points in constrained nonlinear programming. Chapter 5 discusses convexity and its implications in optimization. Chapters 6 and 7 introduce the MM and the EM algorithms widely used in statistics. Chapters 8 and 9 discuss Newton’s method and its offshoots, quasi-Newton algorithms and the method of conjugate gradients. Chapter 10 summarizes convergence results, and Chapter 11 briefly surveys convex programming, duality, and Dykstra’s algorithm.

Kenneth Lange is the Rosenfeld Professor of Computational Genetics in the Departments of Biomathematics and Human Genetics at the UCLA School of Medicine. He is also Interim Chair of the Department of Human Genetics. At various times during his career, he has held appointments at the University of New Hampshire, MIT, Harvard, the University of Michigan, and the University of Helsinki. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer-Verlag previously published his books Mathematical and Statistical Methods for Genetic Analysis, 2nd ed., Numerical Analysis for Statisticians, and Applied Probability.

$$ Buy "Optimization (Springer Texts in Statistics)" on Amazon $$

Please check the description for download links if any or do a search to find alternative books.

Can't Download?
Please search mirrors if you can't find download links for "Optimization (Springer Texts in Statistics)" in "Description" and someone else may update the links. Check the comments when back to find any updates.

Search Mirrors
Maybe some mirror pages will be helpful, search this book at top of this page or click here to find more info.

1. Ebooks list page : 1473
2. Mathematical Statistics: A Unified Introduction (Springer Texts in Statistics)
3. An R and S-Plus Companion to Multivariate Analysis (Springer Texts in Statistics)
4. Modeling Longitudinal Data (Springer Texts in Statistics)
5. Elements of Large-Sample Theory (Springer Texts in Statistics)
6. An Introduction to Bayesian Analysis: Theory and Methods (Springer Texts in Statistics)
7. Bayesian Core: A Practical Approach to Computational Bayesian Statistics (Springer Texts in Statisti
8. Mathematical Statistics (Springer Series in Statistics)
9. Mathematical Statistics (Springer Series in Statistics)
10. Optimization Theory and Methods: Nonlinear Programming (Springer Optimization and Its Applications)
11. [request_ebook] Handbook of Test Problems in Local and Global Optimization (Nonconvex Optimization and Its Applications)
12. Foundations of Modern Probability (Springer Series in Statistics. Probability an
13. Introduction to Optimization (Texts in Applied Mathematics)
14. Introduction to Topological Manifolds (Graduate Texts in Mathematics)
15. Analytic Number Theory (Graduate Texts in Mathematics)
16. Springer Handbook of Engineering Statistics