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Optimization

  • Kenneth Lange

Part of the Springer Texts in Statistics book series (STS, volume 95)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Kenneth Lange
    Pages 1-21
  3. Kenneth Lange
    Pages 23-52
  4. Kenneth Lange
    Pages 53-74
  5. Kenneth Lange
    Pages 75-105
  6. Kenneth Lange
    Pages 107-135
  7. Kenneth Lange
    Pages 137-170
  8. Kenneth Lange
    Pages 171-183
  9. Kenneth Lange
    Pages 185-219
  10. Kenneth Lange
    Pages 221-244
  11. Kenneth Lange
    Pages 245-272
  12. Kenneth Lange
    Pages 273-290
  13. Kenneth Lange
    Pages 291-312
  14. Kenneth Lange
    Pages 313-339
  15. Kenneth Lange
    Pages 341-381
  16. Kenneth Lange
    Pages 383-414
  17. Kenneth Lange
    Pages 415-444
  18. Kenneth Lange
    Pages 445-472
  19. Back Matter
    Pages 473-529

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. 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.

Keywords

Convexity Differentiation Gauge Integral Integration Optimization Statistical variance

Authors and affiliations

  • Kenneth Lange
    • 1
  1. 1.Biomathematics, Human Genetics, StatisticsUniversity of CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-5838-8
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-5837-1
  • Online ISBN 978-1-4614-5838-8
  • Series Print ISSN 1431-875X
  • Buy this book on publisher's site