Linear and Nonlinear Programming

ISBN-10: 0387745025
ISBN-13: 9780387745022
Edition: 3rd 2008
List price: $109.00 Buy it from $91.99
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Description: This edition has been updated with recent optimisation methods. The authors have written chapters and chapter material on a number of these areas including interior point methods. It is designed for either self-study by professionals or classroom  More...

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Book details

List price: $109.00
Edition: 3rd
Copyright year: 2008
Publisher: Springer
Publication date: 7/7/2008
Binding: Hardcover
Pages: 546
Size: 6.25" wide x 9.50" long x 1.75" tall
Weight: 2.486
Language: English

This edition has been updated with recent optimisation methods. The authors have written chapters and chapter material on a number of these areas including interior point methods. It is designed for either self-study by professionals or classroom work at undergraduate or graduate level for technical students.

Introduction
Optimization
Types of Problems
Size of Problems
Iterative Algorithms and Convergence
Linear Programming
Basic Properties of Linear Programs
Introduction
Examples of Linear Programming Problems
Basic Solutions
The Fundamental Theorem of Linear Programming
Relations to Convexity
Exercises
The Simplex Method
Pivots
Adjacent Extreme Points
Determining a Minimum Feasible Solution
Computational Procedure-Simplex Method
Artificial Variables
Matrix Form of the Simplex Method
The Revised Simplex Method
The Simplex Method and LU Decomposition
Decomposition
Summary
Exercises
Duality
Dual Linear Programs
The Duality Theorem
Relations to the Simplex Procedure
Sensitivity and Complementary Slackness
The Dual Simplex Method
The Primal-Dual Algorithm
Reduction of Linear Inequalities
Exercises
Interior-Point Methods
Elements of Complexity Theory
The Simplex Method is not Polynomial-Time
The Ellipsoid Method
The Analytic Center
The Central Path
Solution Strategies
Termination and Initialization
Summary
Exercises
Transportation and Network Flow Problems
The Transportation Problem
Finding a Basic Feasible Solution
Basis Triangularity
Simplex Method for Transportation Problems
The Assignment Problem
Basic Network Concepts
Minimum Cost Flow
Maximal Flow
Summary
Exercises
Unconstrained Problems
Basic Properties of Solutions and Algorithms
First-Order Necessary Conditions
Examples of Unconstrained Problems
Second-Order Conditions
Convex and Concave Functions
Minimization and Maximization of Convex Functions
Zero-Order Conditions
Global Convergence of Descent Algorithms
Speed of Convergence
Summary
Exercises
Basic Descent Methods
Fibonacci and Golden Section Search
Line Search by Curve Fitting
Global Convergence of Curve Fitting
Closedness of Line Search Algorithms
Inaccurate Line Search
The Method of Steepest Descent
Applications of the Theory
Newton's Method
Coordinate Descent Methods
Spacer Steps
Summary
Exercises
Conjugate Direction Methods
Conjugate Directions
Descent Properties of the Conjugate Direction Method
The Conjugate Gradient Method
The C-G Method as an Optimal Process
The Partial Conjugate Gradient Method
Extension to Nonquadratic Problems
Parallel Tangents
Exercises
Quasi-Newton Methods
Modified Newton Method
Construction of the Inverse
Davidon-Fletcher-Powell Method
The Broyden Family
Convergence Properties
Scaling
Memoryless Quasi-Newton Methods
Combination of Steepest Descent and Newton's Method
Summary
Exercises
Constrained Minimization
Constrained Minimization Conditions
Constraints
Tangent Plane
First-Order Necessary Conditions (Equality Constraints)
Examples
Second-Order Conditions
Eigenvalues in Tangent Subspace
Sensitivity
Inequality Constraints
Zero-Order Conditions and Lagrange Multipliers
Summary
Exercises
Primal Methods
Advantage of Primal Methods
Feasible Direction Methods
Active Set Methods
The Gradient Projection Method
Convergence Rate of the Gradient Projection Method
The Reduced Gradient Method
Convergence Rate of the Reduced Gradient Method
Variations
Summary
Exercises
Penalty and Barrier Methods
Penalty Methods
Barrier Methods
Properties of Penalty and Barrier Functions
Newton's Method and Penalty Functions
Conjugate Gradients and Penalty Methods
Normalization of Penalty Functions
Penalty Functions and Gradient Projection
Exact Penalty Functions
Summary
Exercises
Dual and Cutting Plane Methods
Global Duality
Local Duality
Dual Canonical Convergence Rate
Separable Problems
Augmented Lagrangians
The Dual Viewpoint
Cutting Plane Methods
Kelley's Convex Cutting Plane Algorithm
Modifications
Exercises
Primal-Dual Methods
The Standard Problem
Strategies
A Simple Merit Function
Basic Primal-Dual Methods
Modified Newton Methods
Descent Properties
Rate of Convergence
Interior Point Methods
Semidefinite Programming
Summary
Exercises
Mathematical Review
Sets
Matrix Notation
Spaces
Eigenvalues and Quadratic Forms
Topological Concepts
Functions
Convex Sets
Basic Definitions
Hyperplanes and Polytopes
Separating and Supporting Hyperplanes
Extreme Points
Gaussian Elimination
Bibliography
Index

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