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

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