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Table of contents

  1. Front Matter
    Pages i-xiii
  2. Kenneth Lange
    Pages 1-17
  3. Kenneth Lange
    Pages 19-41
  4. Kenneth Lange
    Pages 43-68
  5. Kenneth Lange
    Pages 69-91
  6. Kenneth Lange
    Pages 93-117
  7. Kenneth Lange
    Pages 119-136
  8. Kenneth Lange
    Pages 137-154
  9. Kenneth Lange
    Pages 155-173
  10. Kenneth Lange
    Pages 175-190
  11. Kenneth Lange
    Pages 191-206
  12. Kenneth Lange
    Pages 207-231
  13. Back Matter
    Pages 233-255

About this book

Introduction

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 and can serve as a bridge to more advanced treatises on nonlinear and convex programming. 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, Second Edition, Numerical Analysis for Statisticians, and Applied Probability.

Keywords

Analysis Excel Random variable Statistical Methods Stochastic Processes algorithms expectation–maximization algorithm linear algebra linear optimization modeling nonlinear optimization optimization

Authors and affiliations

  • Kenneth Lange
    • 1
  1. 1.Department of Biomathematics and Human GeneticsUCLA School of MedicineLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4182-7
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-1910-6
  • Online ISBN 978-1-4757-4182-7
  • Series Print ISSN 1431-875X
  • Buy this book on publisher's site