Differentiable Optimization and Equation Solving

A Treatise on Algorithmic Science and the Karmarkar Revolution

  • John Lawrence Nazareth

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Foundations

    1. Front Matter
      Pages 1-1
  3. Lessons from One Dimension

    1. Front Matter
      Pages 47-47
    2. Pages 49-55
  4. Choosing the Right Diagonal Scale

    1. Front Matter
      Pages 81-81
    2. Pages 83-93
  5. Linear Programming Post-Karmarkar

    1. Front Matter
      Pages 115-115
  6. Algorithmic Science

    1. Front Matter
      Pages 165-165
    2. Pages 167-177

About this book

Introduction

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 the resulting, dramatic reorganization that has occurred in one of these areas: algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. The book is aimed at readers familiar with advanced calculus, numerical analysis, in particular numerical linear algebra, the theory and algorithms of linear and nonlinear programming, and the fundamentals of computer science, in particular, computer programming and the basic models of computation and complexity theory.

"Very fine monograph...filled with great insights."

-Joseph F. Traub, Columbia University

Keywords

algorithms complexity linear algebra linear optimization nonlinear optimization optimization

Authors and affiliations

  • John Lawrence Nazareth
    • 1
    • 2
  1. 1.Department of Pure and Applied MathematicsWashington State UniversityPullmanUSA
  2. 2.Department of Applied MathematicsUniversity of WashingtonSeattleWAUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97521
  • Copyright Information John Lawrence Nazareth 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95572-8
  • Online ISBN 978-0-387-21788-8
  • Series Print ISSN 1613-5237
  • About this book