Ebook: Differentiable Optimization and Equation Solving: A Treatise on Algorithmic Science and the Karmarkar Revolution
Author: John Lawrence Nazareth (auth.)
- Tags: Algorithms, Optimization
- Series: CMS Books in Mathematics
- Year: 2003
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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
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
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:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
The Karmarkar Revolution....Pages 3-10
The Newton-Cauchy Method....Pages 11-24
Euler-Newton and Lagrange-NC Methods....Pages 25-45
Front Matter....Pages 47-47
A Misleading Paradigm....Pages 49-55
CG and the Line Search....Pages 57-72
Gilding the Nelder—Mead Lily....Pages 73-79
Front Matter....Pages 81-81
Historical Parallels....Pages 83-93
LP from the Newton-Cauchy Perspective....Pages 95-102
Diagonal Metrics and the QC Method....Pages 103-113
Front Matter....Pages 115-115
LP from the Euler-Newton Perspective....Pages 117-145
Log-Barrier Transformations....Pages 147-153
Karmarkar Potentials and Algorithms....Pages 155-164
Front Matter....Pages 165-165
Algorithmic Principles....Pages 167-177
Multialgorithms: A New Paradigm....Pages 179-203
An Emerging Discipline....Pages 205-223
Back Matter....Pages 225-256
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:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
The Karmarkar Revolution....Pages 3-10
The Newton-Cauchy Method....Pages 11-24
Euler-Newton and Lagrange-NC Methods....Pages 25-45
Front Matter....Pages 47-47
A Misleading Paradigm....Pages 49-55
CG and the Line Search....Pages 57-72
Gilding the Nelder—Mead Lily....Pages 73-79
Front Matter....Pages 81-81
Historical Parallels....Pages 83-93
LP from the Newton-Cauchy Perspective....Pages 95-102
Diagonal Metrics and the QC Method....Pages 103-113
Front Matter....Pages 115-115
LP from the Euler-Newton Perspective....Pages 117-145
Log-Barrier Transformations....Pages 147-153
Karmarkar Potentials and Algorithms....Pages 155-164
Front Matter....Pages 165-165
Algorithmic Principles....Pages 167-177
Multialgorithms: A New Paradigm....Pages 179-203
An Emerging Discipline....Pages 205-223
Back Matter....Pages 225-256
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