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Engineering Optimization Methods and Applications

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ISBN-10: 0471558141

ISBN-13: 9780471558149

Edition: 2nd 2006 (Revised)

Authors: A. Ravindran, Ken M. Ragsdell, Gintaras V. Reklaitis

List price: $190.95
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Description:

Focusing on techniques and strategies useful in engineering design, operations, and analysis, this basic text introduces and develops the practical aspects of optimization methods. It surveys all the important families of optimization methods, from those applicable to the minimization of a single-variable function to those most suited for large-scale nonlinear constrained problems.
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Book details

List price: $190.95
Edition: 2nd
Copyright year: 2006
Publisher: John Wiley & Sons, Incorporated
Publication date: 5/19/2006
Binding: Hardcover
Pages: 688
Size: 6.48" wide x 9.51" long x 1.56" tall
Weight: 2.332
Language: English

A. RAVINDRAN, PhD, is Professor of Industrial and Manufacturing Engineering at Penn State University in University Park, Pennsylvania.K. M. RAGSDELL, PhD, is Professor of Engineering Management at the University of Missouri in Rolla, Missouri.G. V. REKLAITIS, PhD, is Edward W. Comings Professor of Chemical Engineering at Purdue University in West Lafayette, Indiana.

Preface
Introduction to Optimization
Requirements for the Application of Optimization Methods
Defining the System Boundaries
Performance Criterion
Independent Variables
System Model
Applications of Optimization in Engineering
Design Applications
Operations and Planning Applications
Analysis and Data Reduction Applications
Classical Mechanics Applications
Taguchi System of Quality Engineering
Structure of Optimization Problems
Scope of This Book
References
Functions of a Single Variable
Properties of Single-Variable Functions
Optimality Criteria
Region Elimination Methods
Bounding Phase
Interval Refinement Phase
Comparison of Region Elimination Methods
Polynomial Approximation or Point Estimation Methods
Quadratic Estimation Methods
Successive Quadratic Estimation Method
Methods Requiring Derivatives
Newton-Raphson Method
Bisection Method
Secant Method
Cubic Search Method
Comparison of Methods
Summary
References
Problems
Functions of Several Variables
Optimality Criteria
Direct-Search Methods
The S[superscript 2] (Simplex Search) Method
Hooke-Jeeves Pattern Search Method
Powell's Conjugate Direction Method
Gradient-Based Methods
Cauchy's Method
Newton's Method
Modified Newton's Method
Marquardt's Method
Conjugate Gradient Methods
Quasi-Newton Methods
Trust Regions
Gradient-Based Algorithm
Numerical Gradient Approximations
Comparison of Methods and Numerical Results
Summary
References
Problems
Linear Programming
Formulation of Linear Programming Models
Graphical Solution of Linear Programs in Two Variables
Linear Program in Standard Form
Handling Inequalities
Handling Unrestricted Variables
Principles of the Simplex Method
Minimization Problems
Unbounded Optimum
Degeneracy and Cycling
Use of Artificial Variables
Two-Phase Simplex Method
Computer Solution of Linear Programs
Computer Codes
Computational Efficiency of the Simplex Method
Sensitivity Analysis in Linear Programming
Applications
Additional Topics in Linear Programming
Duality Theory
Dual Simplex Method
Interior Point Methods
Integer Programming
Goal Programming
Summary
References
Problems
Constrained Optimality Criteria
Equality-Constrained Problems
Lagrange Multipliers
Economic Interpretation of Lagrange Multipliers
Kuhn-Tucker Conditions
Kuhn-Tucker Conditions or Kuhn-Tucker Problem
Interpretation of Kuhn-Tucker Conditions
Kuhn-Tucker Theorems
Saddlepoint Conditions
Second-Order Optimality Conditions
Generalized Lagrange Multiplier Method
Generalization of Convex Functions
Summary
References
Problems
Transformation Methods
Penalty Concept
Various Penalty Terms
Choice of Penalty Parameter R
Algorithms, Codes, and Other Contributions
Method of Multipliers
Penalty Function
Multiplier Update Rule
Penalty Function Topology
Termination of the Method
MOM Characteristics
Choice of R-Problem Scale
Variable Bounds
Other MOM-Type Codes
Summary
References
Problems
Constrained Direct Search
Problem Preparation
Treatment of Equality Constraints
Generation of Feasible Starting Points
Adaptations of Unconstrained Search Methods
Difficulties in Accommodating Constraints
Complex Method
Discussion
Random-Search Methods
Direct Sampling Procedures
Combined Heuristic Procedures
Discussion
Summary
References
Problems
Linearization Methods for Constrained Problems
Direct Use of Successive Linear Programs
Linearly Constrained Case
General Nonlinear Programming Case
Discussion and Applications
Separable Programming
Single-Variable Functions
Multivariable Separable Functions
Linear Programming Solutions of Separable Problems
Discussion and Applications
Summary
References
Problems
Direction Generation Methods Based on Linearization
Method of Feasible Directions
Basic Algorithm
Active Constraint Sets and Jamming
Discussion
Simplex Extensions for Linearly Constrained Problems
Convex Simplex Method
Reduced Gradient Method
Convergence Acceleration
Generalized Reduced Gradient Method
Implicit Variable Elimination
Basic GRG Algorithm
Extensions of Basic Method
Computational Considerations
Design Application
Problem Statement
General Formulation
Model Reduction and Solution
Summary
References
Problems
Quadratic Approximation Methods for Constrained Problems
Direct Quadratic Approximation
Quadratic Approximation of the Lagrangian Function
Variable Metric Methods for Constrained Optimization
Discussion
Problem Scaling
Constraint Inconsistency
Modification of H[superscript (t)]
Comparison of GRG with CVM
Summary
References
Problems
Structured Problems and Algorithms
Integer Programming
Formulation of Integer Programming Models
Solution of Integer Programming Problems
Guidelines on Problem Formulation and Solution
Quadratic Programming
Applications of Quadratic Programming
Kuhn-Tucker Conditions
Complementary Pivot Problems
Goal Programming
Summary
References
Problems
Comparison of Constrained Optimization Methods
Software Availability
A Comparison Philosophy
Brief History of Classical Comparative Experiments
Preliminary and Final Results
Summary
References
Strategies for Optimization Studies
Model Formulation
Levels of Modeling
Types of Models
Problem Implementation
Model Assembly
Preparation for Solution
Execution Strategies
Solution Evaluation
Solution Validation
Sensitivity Analysis
Summary
References
Problems
Engineering Case Studies
Optimal Location of Coal-Blending Plants by Mixed-Integer Programming
Problem Description
Model Formulation
Results
Optimization of an Ethylene Glycol-Ethylene Oxide Process
Problem Description
Model Formulation
Problem Preparation
Discussion of Optimization Runs
Optimal Design of a Compressed Air Energy Storage System
Problem Description
Model Formulation
Numerical Results
Discussion
Summary
References
Review of Linear Algebra
Set Theory
Vectors
Matrices
Matrix Operations
Determinant of a Square Matrix
Inverse of a Matrix
Condition of a Matrix
Sparse Matrix
Quadratic Forms
Principal Minor
Completing the Square
Convex Sets
Convex and Concave Functions
Gauss-Jordan Elimination Scheme
Author Index
Subject Index
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