Author | Nazareth, John Lawrence. author |
---|---|

Title | Differentiable Optimization and Equation Solving [electronic resource] : A Treatise on Algorithmic Science and the Karmarkar Revolution / by John Lawrence Nazareth |

Imprint | New York, NY : Springer New York, 2003 |

Connect to | http://dx.doi.org/10.1007/b97521 |

Descript | XVII, 256 p. 2 illus. online resource |

SUMMARY

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

CONTENT

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 Nelderโ{128}{148}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

Mathematics
Computer mathematics
Algorithms
Mathematical models
Mathematical optimization
Operations research
Management science
Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Modeling and Industrial Mathematics
Operations Research Management Science
Algorithms
Optimization