rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Optimization
  name:
    name part: Lange, Kenneth.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 2004
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xiii, 255 pages)
  abstract: 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 Michi…
  table of contents: Elementary Optimization -- The Seven C's of Analysis -- Differentiation -- Karush-Kuhn-Tucker Theory -- Convexity -- The MM Algorithm -- The EM Algorithm -- Newton's Method -- Conjugate Gradient and Quasi-Newton -- Analysis of Convergence -- Convex Programming.
  note: by Kenneth Lange.
  note: Electronic resource.
  subject:
    topic: Statistics
  subject:
    topic: Mathematical optimization
  subject:
    topic: Mathematical statistics
  subject:
    topic: Operations research
  subject:
    topic: Mathematical optimization
  subject:
    topic: Mathematical statistics
  subject:
    topic: Operations research
  subject:
    topic: Statistics
  classification: QA276-280
  classification: 519.5
  related item:
    title info:
      title: Springer texts in statistics
  identifier: 9781475741827 (electronic bk.)
  identifier: 1475741820 (electronic bk.)
  identifier: 9781441919106
  identifier: 1441919104
  identifier: 1475741820
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130128
    record change date: 20260422180254.3
    record identifier: in00003558256
    language of cataloging:
      language term: eng