- Cover
- Preface
- Acknowledgment
- About the Author
- About the Companion Website
- 1 Introduction to Optimization
- 1.1 Introduction
- 1.2 Historical Development
- 1.3 Engineering Applications of Optimization
- 1.4 Statement of An Optimization Problem
- 1.5 Classification of Optimization Problems
- 1.6 Optimization Techniques
- 1.7 Engineering Optimization Literature
- 1.8 Solutions Using MATLAB
- References and Bibliography
- Review Questions
- Problems
- 2 Classical Optimization Techniques
- 2.1 Introduction
- 2.2 Single‐Variable Optimization
- 2.3 Multivariable Optimization with no Constraints
- 2.4 Multivariable Optimization with Equality Constraints
- 2.5 Multivariable Optimization with Inequality Constraints
- 2.6 Convex Programming Problem
- References and Bibliography
- Review Questions
- Problems
- 3 Linear Programming I: Simplex Method
- 3.1 Introduction
- 3.2 Applications of Linear Programming
- 3.3 Standard form of a Linear Programming Problem
- 3.4 Geometry of Linear Programming Problems
- 3.5 Definitions and Theorems
- 3.6 Solution of a System of Linear Simultaneous Equations
- 3.7 Pivotal Reduction of a General System of Equations
- 3.8 Motivation of the Simplex Method
- 3.9 Simplex Algorithm
- 3.10 Two Phases of the Simplex Method
- 3.11 Solutions Using MATLAB
- References and Bibliography
- Review Questions
- Problems
- 4 Linear Programming II: Additional Topics and Extensions
- 4.1 Introduction
- 4.2 Revised Simplex Method
- 4.3 Duality in Linear Programming
- 4.4 Decomposition Principle
- 4.5 Sensitivity or Postoptimality Analysis
- 4.6 Transportation Problem
- 4.7 Karmarkar's Interior Method
- 4.8 Quadratic Programming
- 4.9 Solutions Using Matlab
- References and Bibliography
- Review Questions
- Problems
- 5 Nonlinear Programming I: One‐Dimensional Minimization Methods
- 5.1 Introduction
- 5.2 Unimodal Function
- 5.3 Unrestricted Search
- 5.4 Exhaustive Search
- 5.5 Dichotomous Search
- 5.6 Interval Halving Method
- 5.7 Fibonacci Method
- 5.8 Golden Section Method
- 5.9 Comparison of Elimination Methods
- 5.10 Quadratic Interpolation Method
- 5.11 Cubic Interpolation Method
- 5.12 Direct Root Methods
- 5.13 Practical Considerations
- 5.14 Solutions Using MATLAB
- References and Bibliography
- Review Questions
- Problems
- 6 Nonlinear Programming II: Unconstrained Optimization Techniques
- 6.1 Introduction
- 6.2 Random Search Methods
- 6.3 Grid Search Method
- 6.4 Univariate Method
- 6.5 Pattern Directions
- 6.6 Powell's Method
- 6.7 Simplex Method
- 6.8 Gradient of a Function
- 6.9 Steepest Descent (CAuchy) Method
- 6.10 Conjugate Gradient (FLetcher–REeves) Method
- 6.11 Newton's Method
- 6.12 MArquardt Method
- 6.13 Quasi‐Newton Methods
- 6.14 DAvidon–FLetcher–POwell Method
- 6.15 BRoyden–FLetcher–GOldfarb–SHanno Method
- 6.16 Test Functions
- 6.17 Solutions Using Matlab
- References and Bibliography
- Review Questions
- Problems
- 7 Nonlinear Programming III: Constrained Optimization Techniques
- 7.1 Introduction
- 7.2 Characteristics of a Constrained Problem
- 7.3 Random Search Methods
- 7.4 Complex Method
- 7.5 Sequential Linear Programming
- 7.6 Basic Approach in the Methods of Feasible Directions
- 7.7 Zoutendijk's Method of Feasible Directions
- 7.8 Rosen's Gradient Projection Method
- 7.9 Generalized Reduced Gradient Method
- 7.10 Sequential Quadratic Programming
- 7.11 Transformation Techniques
- 7.12 Basic Approach of the Penalty Function Method
- 7.13 Interior Penalty Function Method
- 7.14 Convex Programming Problem
- 7.15 Exterior Penalty Function Method
- 7.16 Extrapolation Techniques in the Interior Penalty Function Method
- 7.17 Extended Interior Penalty Function Methods
- 7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints
- 7.19 Penalty Function Method for Parametric Constraints
- 7.20 Augmented Lagrange Multiplier Method
- 7.21 Checking the Convergence of Constrained Optimization Problems
- 7.22 Test Problems
- 7.23 Solutions Using MATLAB
- References and Bibliography
- Review Questions
- Problems
- 8 Geometric Programming
- 8.1 Introduction
- 8.2 Posynomial
- 8.3 Unconstrained Minimization Problem
- 8.4 Solution of an Unconstrained Geometric Programming Program using Differential Calculus
- 8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic–Geometric Inequality
- 8.6 Primal–dual Relationship and Sufficiency Conditions in the Unconstrained Case
- 8.7 Constrained Minimization
- 8.8 Solution of a Constrained Geometric Programming Problem
- 8.9 Primal and Dual Programs in the Case of Less‐than Inequalities
- 8.10 Geometric Programming with Mixed Inequality Constraints
- 8.11 Complementary Geometric Programming
- 8.12 Applications of Geometric Programming
- References and Bibliography
- Review Questions
- Problems
- 9 Dynamic Programming
- 9.1 Introduction
- 9.2 Multistage Decision Processes
- 9.3 Concept of Suboptimization and Principle of Optimality
- 9.4 Computational Procedure in Dynamic Programming
- 9.5 Example Illustrating the Calculus Method of Solution
- 9.6 Example Illustrating the Tabular Method of Solution
- 9.7 Conversion of a Final Value Problem into an Initial Value Problem
- 9.8 Linear Programming as a Case of Dynamic Programming
- 9.9 Continuous Dynamic Programming
- 9.10 Additional Applications
- References and Bibliography
- Review Questions
- Problems
- 10 Integer Programming
- 10.1 Introduction
- 10.2 Graphical Representation
- 10.3 Gomory's Cutting Plane Method
- 10.4 Balas' Algorithm for Zero–One Programming Problems
- 10.5 Integer Polynomial Programming
- 10.6 Branch‐and‐Bound Method
- 10.7 Sequential Linear Discrete Programming
- 10.8 Generalized Penalty Function Method
- 10.9 Solutions Using MATLAB
- References and Bibliography
- Review Questions
- Problems
- 11 Stochastic Programming
- 12 Optimal Control and Optimality Criteria Methods
- 13 Modern Methods of Optimization
- 14 Metaheuristic Optimization Methods
- 15 Practical Aspects of Optimization
- 15.1 Introduction
- 15.2 Reduction of Size of an Optimization Problem
- 15.3 Fast Reanalysis Techniques
- 15.4 Derivatives of Static Displacements and Stresses
- 15.5 Derivatives of Eigenvalues and Eigenvectors
- 15.6 Derivatives of Transient Response
- 15.7 Sensitivity of Optimum Solution to Problem Parameters
- References and Bibliography
- Review Questions
- Problems
- 16 Multilevel and Multiobjective Optimization
- 17 Solution of Optimization Problems Using MATLAB
- 17.1 Introduction
- 17.2 Solution of General Nonlinear Programming Problems
- 17.3 Solution of Linear Programming Problems
- 17.4 Solution of LP Problems Using Interior Point Method
- 17.5 Solution of Quadratic Programming Problems
- 17.6 Solution of One‐Dimensional Minimization Problems
- 17.7 Solution of Unconstrained Optimization Problems
- 17.8 Solution of Constrained Optimization Problems
- 17.9 Solution of Binary Programming Problems
- 17.10 Solution of Multiobjective Problems
- References and Bibliography
- Problems
- Appendix A: Appendix AConvex and Concave FunctionsConvex and Concave Functions
- Appendix B: Appendix BSome Computational Aspects of OptimizationSome Computational Aspects of Optimization
- Appendix C: Appendix CIntroduction to MATLAB®Introduction to MATLAB®
- Answers to Selected Problems
- Index
- End User License Agreement
Acknowledgment
I would like to acknowledge that the thousands of hours spent in writing/revising this book were actually the hours that would otherwise have been spent with my wife Kamala and other family members. My heartfelt gratitude is for Kamala's patience and sacrifices which could never be measured or quantified.
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