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Other titles in the CMS Books in Mathematics series:
Differentiable Optimization and Equation Solving: A Treatise on Algorithmic Science and the Karmarkar Revolution (CMS Books in Mathematics)by John L. Nazareth
Synopses & ReviewsPublisher Comments: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 worldwide 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 equationsolving, 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. J.L. Nazareth is a Professor in the Department of Pure and Applied Mathematics at Washington State University. He is the author of two books previously published by SpringerVerlag, DLP and Extensions: An Optimization Model and Decision Support System (2001) and The NewtonCauchy Framework: A Unified Approach to Unconstrained Nonlinear Minimization (1994).
Synopsis:An overview of the dramatic reorganization in reaction to N. Karmakar's seminal 1984 paper on algorithmic linear programming in the area of algorithmic differentiable optimization and equationsolving, or, more simply, algorithmic differentiable programming. Aimed at readers familiar with advanced calculus and numerical analysis.
Table of ContentsThe Karmarkar Revolution * The NewtonCauchy Method * EulerNewton and LagrangeNC Methods * A Misleading Paradigm * CG and the Line Search * Gilding the NelderMead Lily * Historic Parallels * LP from the NewtonCauchy Perspective * Diagonal Metrics and the QC Method * LP from the EulerNewton Perspective * LogBarrier Transformations * Karmarkar Potentials and Algorithms * Algorithmic Principles * Multialgorithms: A New Paradigm * An Emerging Discipline * Bibliography * Index
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Science and Mathematics » Mathematics » Applied


