The Karmarkar Revolution * The Newton-Cauchy Method * Euler-Newton and Lagrange-NC Methods * A Misleading Paradigm * CG and the Line Search * Gilding the Nelder-Mead Lily * Historic Parallels * LP from the Newton-Cauchy Perspective * Diagonal Metrics and the QC Method * LP from the Euler-Newton Perspective * Log-Barrier Transformations * Karmarkar Potentials and Algorithms * Algorithmic Principles * Multialgorithms: A New Paradigm * An Emerging Discipline * Bibliography * Index
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.