Differentiable Optimization and Equation Solving

A Treatise on Algorithmic Science and the Karmarkar Revolution

Authors:

ISBN: 978-0-387-95572-8 (Print) 978-0-387-21788-8 (Online)

Table of contents (15 chapters)

  1. Foundations

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-10

      The Karmarkar Revolution

    3. No Access

      Book Chapter

      Pages 11-24

      The Newton-Cauchy Method

    4. No Access

      Book Chapter

      Pages 25-45

      Euler-Newton and Lagrange-NC Methods

  2. Lessons from One Dimension

    1. Front Matter

      Pages 47-47

    2. No Access

      Book Chapter

      Pages 49-55

      A Misleading Paradigm

    3. No Access

      Book Chapter

      Pages 57-72

      CG and the Line Search

    4. No Access

      Book Chapter

      Pages 73-79

      Gilding the Nelder—Mead Lily

  3. Choosing the Right Diagonal Scale

    1. Front Matter

      Pages 81-81

    2. No Access

      Book Chapter

      Pages 83-93

      Historical Parallels

    3. No Access

      Book Chapter

      Pages 95-102

      LP from the Newton-Cauchy Perspective

    4. No Access

      Book Chapter

      Pages 103-113

      Diagonal Metrics and the QC Method

  4. Linear Programming Post-Karmarkar

    1. Front Matter

      Pages 115-115

    2. No Access

      Book Chapter

      Pages 117-145

      LP from the Euler-Newton Perspective

    3. No Access

      Book Chapter

      Pages 147-153

      Log-Barrier Transformations

    4. No Access

      Book Chapter

      Pages 155-164

      Karmarkar Potentials and Algorithms

  5. Algorithmic Science

    1. Front Matter

      Pages 165-165

    2. No Access

      Book Chapter

      Pages 167-177

      Algorithmic Principles

    3. No Access

      Book Chapter

      Pages 179-203

      Multialgorithms: A New Paradigm

    4. No Access

      Book Chapter

      Pages 205-223

      An Emerging Discipline