Differentiable Optimization and Equation Solving: A Treatise on Algorithmic Science and the Karmarkar Revolution

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Springer Science & Business Media, Mar 5, 2003 - Mathematics - 256 pages
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. 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 Springer-Verlag, DLP and Extensions: An Optimization Model and Decision Support System (2001) and The Newton-Cauchy Framework: A Unified Approach to Unconstrained Nonlinear Minimization (1994).
 

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Contents

1
3
Algorithmic Science
9
2
11
EulerNewton and LagrangeNC Methods
17
2 1 Newton 2 2 2 QuasiNewton 2 2 3 Limited Memory
22
Introduction The EN Method
28
The LNC Method
35
Notes
45
LogBarrier Transformations
146
Karmarkar Potentials and Algorithms
155
Algorithmic Principles
166
A New Paradigm
179
1 1 Notation 12 1 2 Unweighted Case 12 1 3 Weighted Case A PotentialReduction Algorithm
186
3
187
6
193
An Emerging Discipline
204

5
56
6
73
Choosing the Right Diagonal Scale
81
Notes
113
Linear Programming PostKarmarkar
114
6
122
25
141
32
210
References
225
35
228
118
234
167
238
Index 251
250
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