Engineering Optimization : Theory and Practice
by Rao, Singiresu S.Edition: 4th
Format: Hardcover
Pub. Date: 2009-07-20
Publisher(s): Wiley
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Summary
This is the only book on the market that discusses all the important methods of optimization. All the methods are presented in a simple language in the most comprehensive manner. Nonlinear, linear, geometric, dynamic and stochastic programming techniques are presented with a focus on engineering applications. Other more specialized methods such as optimal control, multiobjective optimization, genetic algorithms, simulated annealing, neural networks and fuzzy optimization methods are also included. In each case examples and cases are presented to show how the mtheod is actually used in the real world.
Author Biography
Singiresu S. Rao, PhD, is a Professor and Chairman of the Department of Mechanical Engineering at the University of Miami. Dr. Rao has published more than 175 technical papers in internationally respected journals and more than 150 papers in conference proceedings in the areas of engineering optimization, reliability-based design, fuzzy systems, uncertainty models, structural and mechanical design, and vibration engineering. He has authored several books, including The Finite Element Method in Engineering, Mechanical Vibrations, Vibration of Continuous Systems, Reliability-Based Design, and Applied Numerical Methods for Engineers and Scientists.
Table of Contents
| Preface | |
| Introduction to Optimization | |
| Introduction | |
| Historical Developments | |
| Engineering Applications of Optimization | |
| Statement of an Optimization Problem | |
| Classification of Optimization Problems | |
| Optimization Techniques | |
| Engineering Optimization Literature | |
| Solution of Optimization Problems Using MATLAB | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Classical Optimization Techniques | |
| Introduction | |
| Single Variable Optimization | |
| Multivariable Optimization with no Constraints | |
| Multivariable Optimization with Equality Constraints | |
| Multivariable Optimization with Inequality Constraints | |
| Convex Programming Problem | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Linear Programming I: Simplex Method | |
| Introduction | |
| Applications of Linear Programming | |
| Standard Form of a Linear Programming Problem | |
| Geometry of Linear Programming Problems | |
| Definitions and Theorems | |
| Solution of a System of Linear Simultaneous Equations | |
| Pivotal Reduction of a General System of Equations | |
| Motivation of the Simplex Method | |
| Simplex Algorithm | |
| Two phases of the Simplex Method | |
| MATLAB Solution of L.P. Problems | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Linear Programming II: Additional Topics and Extensions | |
| Introduction | |
| Revised Simplex Method | |
| Duality in Linear Programming | |
| Decomposition Principle | |
| Sensitivity or Postoptimality Analysis | |
| Transportation Problem | |
| Karmarkar?s Interior Method | |
| Quadratic Programming | |
| MATLAB Solutions | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Nonlinear Programmimg I: One-Dimensional Minimization Methods | |
| Introduction | |
| Unimodal Function | |
| Elimination Methods | |
| Unrestricted Search | |
| Exhaustive Search | |
| Dichotomous Search | |
| Interval Halving Method | |
| Fibonacci Method | |
| Golden Section Method | |
| Comparison of Elimination Methods | |
| Interpolation Methods | |
| Quadratic Interpolation Method | |
| Cubic Interpolation Method | |
| Direct Root Methods | |
| Practical Considerations | |
| MATLAB Solution of One-Dimensional Minimization Problems | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Nonlinear Programming II: Unconstrained Optimization Techniques | |
| Introduction | |
| Direct Search Methods | |
| Random Search Methods | |
| Grid Search Method | |
| Univariate Method | |
| Pattern Directions | |
| Powell's Method | |
| Simplex Mehod | |
| Indirect Search (Descent) Methods | |
| Gradient of a Function | |
| Steepest Descent (Cauchy) Method | |
| Conjugate Gradient (Fletcher-Reeves) Method | |
| Newton's Method | |
| Marquardt Method | |
| Quasi-Newton Methods | |
| Rank 1 Updates | |
| Rank 2 Updates | |
| Davidon-Fletcher-Powell Method | |
| Broydon-Fletcher-Goldfarb-Shanno Method | |
| Test Functions | |
| MATLAB Solution of Unconstrained Optimization Problems | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Nonlinear Programming III: Constrained Optimization Techniques | |
| Introduction | |
| Characteristics of a Constrained Problem | |
| Direct Methods | |
| Random Search Methods | |
| Complex Method | |
| Sequential Linear Programming | |
| Basic Approach in the Methods of Feasible Directions | |
| Zoutendijk's Method of Feasible Directions | |
| Rosen's Gradient Projection Method | |
| Generalized Reduced Gradient Method | |
| Sequential Quadratic Programming | |
| Indirect Methods | |
| Transformation Techniques | |
| Basic Approach of the Penalty Function Method | |
| Interior Penalty Function Method | |
| Convex Programming Problem | |
| Exterior Penalty Function Method | |
| Extrapolation Techniques in the Penalty Function Method | |
| Extended Interior Penalty Function Methods | |
| Penalty Function Method for Problems with Mixed Equality and Inequality Constraints | |
| Penalty Function Method for Parametric Constraints | |
| Augmented Lagrange Multiplier Method | |
| Checking the Convergence of Constrained Optimization Problems | |
| Test Problems | |
| MATLAB Solution of Constrained Optimization Problems | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Geometric Programming | |
| Introduction | |
| Posynomial | |
| Unconstrained Minimization Problem | |
| Solution of an Unconstrained Geometric Programming Problem Using Differential Calculus | |
| Solution of an Unconstrained Geometric Programming Problem Using Arithmetic-Geometric Inequality | |
| Primal-Dual Relationship and Sufficiency Conditions in the Unconstrained Case | |
| Constrained Minimization | |
| Solution of a Constrained Geometric Programming Problem | |
| Primal and Dual Programs in the Case of Less-Than Inequalities | |
| Geometric Programming with Mixed Inequality Constraints | |
| Complementary Geometric Programming | |
| Applications of Geometric Programming | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Dynamic Programming | |
| Introduction | |
| Multistage Decision Processes | |
| Concept of Suboptimization and Principle of Optimality | |
| Computational Procedure in Dynamic Programming | |
| Example Illustrating the Calculus Method of Solution | |
| Example Illustrating the Tabular Method of Solution | |
| Conversion of a Final Value Problem into an Initial Value Problem | |
| Linear Programming as a Case of Dynamic Programming | |
| Continuous Dynamic Programming | |
| Additional Applications | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Integer Programming | |
| Introduction | |
| Integer Linear Programming | |
| Graphical Representation | |
| Gomory's Cutting Plane Method | |
| Balas' Algorithm for Zero-One Programming Problems | |
| Integer Nonlinear Programming | |
| Integer Polynomial Programming | |
| Branch-and-Bound Method | |
| Sequential Linear Discrete Programming | |
| Generalized Penalty Function Method | |
| Solution of Binary Programming Problems Using MATLAB | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Stochastic Programming | |
| Introduction | |
| Basic Concepts of Probability Theory | |
| Stochastic Linear Programming | |
| Stochastic Nonlinear Programming | |
| Stochastic Geometric Programming | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Optimal Control and Optimality Criteria Methods | |
| Introduction | |
| Calculus of Variations | |
| Optimal Control Theory | |
| Optimality Criteria Methods | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Modern Methods of Optimization | |
| Introduction | |
| etic Algorithms | |
| Simulated Annealing | |
| Particle Swarm Optimization | |
| Ant Colony Optimization | |
| Optimization of Fuzzy Systems | |
| Neural-Network-Based Optimization | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Practical Aspects of Optimization | |
| Introduction | |
| Reduction of Size of an Optimization Problem | |
| Fast Reanalysis Techniques | |
| Derivatives of Static Displacements and Stresses | |
| Derivatives of Eigenvalues and Eigenvectors | |
| Derivatives of Transient Response | |
| Sensitivity of Optimum Solution to Problem Parameters | |
| Multilevel Optimization | |
| Parallel Processing | |
| Multiobjective Optimization | |
| Solution of Multiobjective Problems Using MATLAB | |
| References and Bibliography | |
| Review Questions | |
| Problems | |
| Convex and Concave Functions | |
| Some Computational Aspects of Optimization | |
| Choice of Method | |
| Comparison of Unconstrained Methods | |
| Comparison of Constrained Methods | |
| Availability of Computer Programs | |
| Scaling of Design Variables and Constraints | |
| References and Bibliography | |
| Introduction to MATLAB | |
| Features and Special Characters | |
| Defining Matrices in MATLAB | |
| Creating m-files | |
| Optimization Toolbox | |
| Answers to Selected Problems | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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