Beschreibung:
This book gives an overview of the dramatic reorganization that has occurred during the last decade in one area of mathematical programming and numerical computation: algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. The reader is assumed to be familiar with advanced calculus, numerical analysis, the theory and algorithms of linear and nonlinear programming, and the fundamentals of computer science. Thus, this monograph is intended for researchers in optimization and advanced graduate students. But others will find the ideas to be of interest as well.
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.
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
