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| Preface | |
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| Introduction to Optimization | |
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| Introduction | |
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| Historical Developments | |
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| Engineering Applications of Optimization | |
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| Statement of an Optimization Problem | |
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| Classification of Optimization Problems | |
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| Optimization Techniques | |
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| Engineering Optimization Literature | |
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| Solution of Optimization Problems Using MATLAB | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Classical Optimization Techniques | |
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| Introduction | |
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| Single Variable Optimization | |
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| Multivariable Optimization with no Constraints | |
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| Multivariable Optimization with Equality Constraints | |
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| Multivariable Optimization with Inequality Constraints | |
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| Convex Programming Problem | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Linear Programming I: Simplex Method | |
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| Introduction | |
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| Applications of Linear Programming | |
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| Standard Form of a Linear Programming Problem | |
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| Geometry of Linear Programming Problems | |
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| Definitions and Theorems | |
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| Solution of a System of Linear Simultaneous Equations | |
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| Pivotal Reduction of a General System of Equations | |
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| Motivation of the Simplex Method | |
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| Simplex Algorithm | |
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| Two phases of the Simplex Method | |
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| MATLAB Solution of L.P. Problems | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Linear Programming II: Additional Topics and Extensions | |
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| Introduction | |
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| Revised Simplex Method | |
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| Duality in Linear Programming | |
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| Decomposition Principle | |
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| Sensitivity or Postoptimality Analysis | |
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| Transportation Problem | |
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| Karmarkar?s Interior Method | |
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| Quadratic Programming | |
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| MATLAB Solutions | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Nonlinear Programmimg I: One-Dimensional Minimization Methods | |
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| Introduction | |
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| Unimodal Function | |
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| Elimination Methods | |
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| Unrestricted Search | |
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| Exhaustive Search | |
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| Dichotomous Search | |
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| Interval Halving Method | |
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| Fibonacci Method | |
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| Golden Section Method | |
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| Comparison of Elimination Methods | |
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| Interpolation Methods | |
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| Quadratic Interpolation Method | |
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| Cubic Interpolation Method | |
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| Direct Root Methods | |
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| Practical Considerations | |
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| MATLAB Solution of One-Dimensional Minimization Problems | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Nonlinear Programming II: Unconstrained Optimization Techniques | |
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| Introduction | |
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| Direct Search Methods | |
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| Random Search Methods | |
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| Grid Search Method | |
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| Univariate Method | |
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| Pattern Directions | |
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| Powell's Method | |
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| Simplex Mehod | |
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| Indirect Search (Descent) Methods | |
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| Gradient of a Function | |
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| Steepest Descent (Cauchy) Method | |
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| Conjugate Gradient (Fletcher-Reeves) Method | |
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| Newton's Method | |
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| Marquardt Method | |
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| Quasi-Newton Methods | |
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| Rank 1 Updates | |
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| Rank 2 Updates | |
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| Davidon-Fletcher-Powell Method | |
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| Broydon-Fletcher-Goldfarb-Shanno Method | |
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| Test Functions | |
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| MATLAB Solution of Unconstrained Optimization Problems | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Nonlinear Programming III: Constrained Optimization Techniques | |
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| Introduction | |
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| Characteristics of a Constrained Problem | |
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| Direct Methods | |
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| Random Search Methods | |
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| Complex Method | |
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| Sequential Linear Programming | |
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| Basic Approach in the Methods of Feasible Directions | |
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| Zoutendijk's Method of Feasible Directions | |
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| Rosen's Gradient Projection Method | |
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| Generalized Reduced Gradient Method | |
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| Sequential Quadratic Programming | |
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| Indirect Methods | |
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| Transformation Techniques | |
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| Basic Approach of the Penalty Function Method | |
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| Interior Penalty Function Method | |
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| Convex Programming Problem | |
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| Exterior Penalty Function Method | |
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| Extrapolation Techniques in the Penalty Function Method | |
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| Extended Interior Penalty Function Methods | |
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| Penalty Function Method for Problems with Mixed Equality and Inequality Constraints | |
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| Penalty Function Method for Parametric Constraints | |
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| Augmented Lagrange Multiplier Method | |
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| Checking the Convergence of Constrained Optimization Problems | |
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| Test Problems | |
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| MATLAB Solution of Constrained Optimization Problems | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Geometric Programming | |
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| Introduction | |
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| Posynomial | |
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| Unconstrained Minimization Problem | |
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| Solution of an Unconstrained Geometric Programming Problem Using Differential Calculus | |
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| Solution of an Unconstrained Geometric Programming Problem Using Arithmetic-Geometric Inequality | |
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| Primal-Dual Relationship and Sufficiency Conditions in the Unconstrained Case | |
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| Constrained Minimization | |
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| Solution of a Constrained Geometric Programming Problem | |
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| Primal and Dual Programs in the Case of Less-Than Inequalities | |
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| Geometric Programming with Mixed Inequality Constraints | |
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| Complementary Geometric Programming | |
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| Applications of Geometric Programming | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Dynamic Programming | |
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| Introduction | |
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| Multistage Decision Processes | |
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| Concept of Suboptimization and Principle of Optimality | |
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| Computational Procedure in Dynamic Programming | |
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| Example Illustrating the Calculus Method of Solution | |
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| Example Illustrating the Tabular Method of Solution | |
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| Conversion of a Final Value Problem into an Initial Value Problem | |
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| Linear Programming as a Case of Dynamic Programming | |
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| Continuous Dynamic Programming | |
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| Additional Applications | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Integer Programming | |
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| Introduction | |
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| Integer Linear Programming | |
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| Graphical Representation | |
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| Gomory's Cutting Plane Method | |
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| Balas' Algorithm for Zero-One Programming Problems | |
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| Integer Nonlinear Programming | |
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| Integer Polynomial Programming | |
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| Branch-and-Bound Method | |
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| Sequential Linear Discrete Programming | |
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| Generalized Penalty Function Method | |
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| Solution of Binary Programming Problems Using MATLAB | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Stochastic Programming | |
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| Introduction | |
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| Basic Concepts of Probability Theory | |
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| Stochastic Linear Programming | |
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| Stochastic Nonlinear Programming | |
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| Stochastic Geometric Programming | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Optimal Control and Optimality Criteria Methods | |
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| Introduction | |
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| Calculus of Variations | |
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| Optimal Control Theory | |
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| Optimality Criteria Methods | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Modern Methods of Optimization | |
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| Introduction | |
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| etic Algorithms | |
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| Simulated Annealing | |
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| Particle Swarm Optimization | |
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| Ant Colony Optimization | |
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| Optimization of Fuzzy Systems | |
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| Neural-Network-Based Optimization | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Practical Aspects of Optimization | |
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| Introduction | |
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| Reduction of Size of an Optimization Problem | |
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| Fast Reanalysis Techniques | |
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| Derivatives of Static Displacements and Stresses | |
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| Derivatives of Eigenvalues and Eigenvectors | |
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| Derivatives of Transient Response | |
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| Sensitivity of Optimum Solution to Problem Parameters | |
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| Multilevel Optimization | |
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| Parallel Processing | |
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| Multiobjective Optimization | |
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| Solution of Multiobjective Problems Using MATLAB | |
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| References and Bibliography | |
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| Review Questions | |
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| Problems | |
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| Convex and Concave Functions | |
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| Some Computational Aspects of Optimization | |
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| Choice of Method | |
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| Comparison of Unconstrained Methods | |
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| Comparison of Constrained Methods | |
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| Availability of Computer Programs | |
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| Scaling of Design Variables and Constraints | |
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| References and Bibliography | |
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| Introduction to MATLAB | |
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| Features and Special Characters | |
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| Defining Matrices in MATLAB | |
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| Creating m-files | |
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| Optimization Toolbox | |
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| Answers to Selected Problems | |
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| Index | |