Differentiable Optimization and Equation Solving A Treatise on Algorithmic Science and the Karmarkar Revolution

Differentiable Optimization and Equation Solving A Treatise on Algorithmic Science and the Karmarkar Revolution / by John L. Nazareth.

In 1984, N. Karmarkar published a seminal paper on algorithmic linear programming. During the subsequent decade, it stimulated a huge outpouring of new algorithmic results by researchers world-wide in many areas of mathematical programming and numerical computation. This book gives an overview of th...

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Bibliographic Details
Main Author: Nazareth, John L. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2003.
Edition:1st ed. 2003.
Series:CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
Springer eBook Collection.
Subjects:
Computer mathematics.
Mathematical models.
Operations research.
Management science.
Algorithms.
Mathematical optimization.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Foundations
  • The Karmarkar Revolution
  • The Newton-Cauchy Method
  • Euler-Newton and Lagrange-NC Methods
  • Lessons from One Dimension
  • A Misleading Paradigm
  • CG and the Line Search
  • Gilding the Nelder—Mead Lily
  • Choosing the Right Diagonal Scale
  • Historical Parallels
  • LP from the Newton-Cauchy Perspective
  • Diagonal Metrics and the QC Method
  • Linear Programming Post-Karmarkar
  • LP from the Euler-Newton Perspective
  • Log-Barrier Transformations
  • Karmarkar Potentials and Algorithms
  • Algorithmic Science
  • Algorithmic Principles
  • Multialgorithms: A New Paradigm
  • An Emerging Discipline.

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