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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 | |