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

• Main Author: Nazareth, John Lawrence (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2003.
• Series: CMS Books in Mathematics,
• Subjects: Mathematics.; Computer mathematics.; Algorithms.; Mathematical models.; Mathematical optimization.; Operations research.; Management science.; Computational Mathematics and Numerical Analysis.; Mathematical Modeling and Industrial Mathematics.; Operations Research, Management Science.; Optimization.

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...

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.