**PDF Free Download | Engineering Optimization Theory and Practice 4th Edition by Singiresu S. Rao**

## Contents of Engineering Optimization PDF

- Introduction to Optimization
- Historical Development
- Engineering Applications of Optimization
- Statement of an Optimization Problem
- Design Vector
- Design Constraints
- Constraint Surface
- Objective Function
- Objective Function Surfaces
- Classification of Optimization Problems
- Classification Based on the Existence of Constraints
- Classification Based on the Nature of the Design Variables
- Classification Based on the Physical Structure of the Problem
- Classification Based on the Nature of the Equations Involved
- Classification Based on the Permissible Values of the Design Variables
- Classification Based on the Deterministic Nature of the Variables
- Classification Based on the Separability of the Functions
- Classification Based on the Number of Objective Functions
- Optimization Techniques
- Engineering Optimization Literature
- Solution of Optimization Problems Using MATLAB
- Single-Variable Optimization
- Multivariable Optimization with No Constraints
- Semidefinite Case
- Saddle Point
- Multivariable Optimization with Equality Constraints
- Solution by Direct Substitution
- Solution by the Method of Constrained Variation
- Solution by the Method of Lagrange Multipliers
- Multivariable Optimization with Inequality Constraints
- Kuhn–Tucker Conditions
- Constraint Qualification
- Convex Programming Problem
- Linear Programming I: Simplex Method
- 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
- Identifying an Optimal Point
- Improving a Nonoptimal Basic Feasible Solution
- Two Phases of the Simplex Method
- MATLAB Solution of LP Problems
- Linear Programming II: Additional Topics and Extensions
- Revised Simplex Method
- Duality in Linear Programming
- Symmetric Primal–Dual Relations
- General Primal–Dual Relations
- Primal–Dual Relations When the Primal Is in Standard Form
- Duality Theorems
- Dual Simplex Method
- Decomposition Principle
- Sensitivity or Postoptimality Analysis
- Changes in the Right-Hand-Side Constants bi
- Changes in the Cost Coefficients cj
- Addition of New Variables
- Changes in the Constraint Coefficients aij
- Addition of Constraints
- Transportation Problem
- Karmarkar’s Interior Method
- Statement of the Problem
- Conversion of an LP Problem into the Required Form
- Algorithm
- Quadratic Programming
- MATLAB Solutions
- Nonlinear Programming I: One-Dimensional Minimization Methods
- Unimodal Function
- ELIMINATION METHODS
- Unrestricted Search
- Search with Fixed Step Size
- Search with Accelerated Step Size
- 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
- Newton Method
- Quasi-Newton Method
- Secant Method
- Practical Considerations
- How to Make the Methods Efficient and More Reliable
- Implementation in Multivariable Optimization Problems
- Comparison of Methods
- MATLAB Solution of One-Dimensional Minimization Problems
- Nonlinear Programming II: Unconstrained Optimization Techniques
- Classification of Unconstrained Minimization Methods
- General Approach
- Rate of Convergence
- Scaling of Design Variables
- DIRECT SEARCH METHODS
- Random Search Methods
- Random Jumping Method
- Random Walk Method
- Random Walk Method with Direction Exploitation
- Advantages of Random Search Methods
- Grid Search Method
- Univariate Method
- Pattern Directions
- Powell’s Method
- Conjugate Directions
- Algorithm
- Simplex Method
- Reflection
- Expansion
- Contraction
- INDIRECT SEARCH (DESCENT) METHODS
- Gradient of a Function
- Evaluation of the Gradient
- Rate of Change of a Function along a Direction
- Steepest Descent (Cauchy) Method
- Conjugate Gradient (Fletcher–Reeves) Method
- Development of the Fletcher–Reeves Method
- Fletcher–Reeves Method
- Newton’s Method
- Marquardt Method
- Quasi-Newton Methods
- Rank Updates
- Rank Updates
- Davidon–Fletcher–Powell Method
- Broyden–Fletcher–Goldfarb–Shanno Method
- Test Functions
- MATLAB Solution of Unconstrained Optimization Problems
- Nonlinear Programming III: Constrained Optimization Techniques
- 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
- Direction-Finding Problem
- Determination of Step Length
- Termination Criteria
- Rosen’s Gradient Projection Method
- Determination of Step Length
- Generalized Reduced Gradient Method
- Sequential Quadratic Programming
- Derivation
- Solution Procedure
- 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 Interior Penalty Function Method
- Extrapolation of the Design Vector X
- Extrapolation of the Function f
- Extended Interior Penalty Function Methods
- Linear Extended Penalty Function Method
- Quadratic Extended Penalty Function Method
- Penalty Function Method for Problems with Mixed Equality and Inequality
- Constraints
- Interior Penalty Function Method
- Exterior Penalty Function Method
- Penalty Function Method for Parametric Constraints
- Parametric Constraint
- Handling Parametric Constraints
- Augmented Lagrange Multiplier Method
- Equality-Constrained Problems
- Inequality-Constrained Problems
- Mixed Equality–Inequality-Constrained Problems
- Checking the Convergence of Constrained Optimization Problems
- Perturbing the Design Vector
- Testing the Kuhn–Tucker Conditions
- Test Problems
- Design of a Three-Bar Truss
- Design of a Twenty-Five-Bar Space Truss
- Welded Beam Design
- Speed Reducer (Gear Train) Design
- Heat Exchanger Design
- MATLAB Solution of Constrained Optimization Problems
- Geometric Programming
- Posynomial
- Unconstrained Minimization Problem
- Solution of an Unconstrained Geometric Programming Program 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
- Dynamic Programming
- Multistage Decision Processes
- Definition and Examples
- Representation of a Multistage Decision Process
- Conversion of a Nonserial System to a Serial System
- Types of Multistage Decision Problems
- 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
- Design of Continuous Beams
- Optimal Layout (Geometry) of a Truss
- Optimal Design of a Gear Train
- Design of a Minimum-Cost Drainage System
- Integer Programming
- INTEGER LINEAR PROGRAMMING
- Graphical Representation
- Gomory’s Cutting Plane Method
- Concept of a Cutting Plane
- Gomory’s Method for All-Integer Programming Problems
- Gomory’s Method for Mixed-Integer Programming Problems
- Balas’ Algorithm for Zero–One Programming Problems
- INTEGER NONLINEAR PROGRAMMING
- Integer Polynomial Programming
- Representation of an Integer Variable by an Equivalent System of Binary
- Variables
- Conversion of a Zero–One Polynomial Programming Problem into a
- Zero–One LP Problem
- Branch-and-Bound Method
- Sequential Linear Discrete Programming
- Generalized Penalty Function Method
- Solution of Binary Programming Problems Using MATLAB
- Stochastic Programming
- Basic Concepts of Probability Theory
- Definition of Probability
- Random Variables and Probability Density Functions
- Mean and Standard Deviation
- Function of a Random Variable
- Jointly Distributed Random Variables
- Covariance and Correlation
- Functions of Several Random Variables
- Probability Distributions
- Central Limit Theorem
- Stochastic Linear Programming
- Stochastic Nonlinear Programming
- Objective Function
- Constraints
- Stochastic Geometric Programming
- Optimal Control and Optimality Criteria Methods
- Calculus of Variations
- Problem of Calculus of Variations
- Lagrange Multipliers and Constraints
- Generalization
- Optimal Control Theory
- Necessary Conditions for Optimal Control
- Necessary Conditions for a General Problem
- Optimality Criteria Methods
- Optimality Criteria with a Single Displacement Constraint
- Optimality Criteria with Multiple Displacement Constraints
- Reciprocal Approximations
- Modern Methods of Optimization
- Genetic Algorithms
- Representation of Design Variables
- Representation of Objective Function and Constraints
- Genetic Operators
- Algorithm
- Numerical Results
- Simulated Annealing
- Procedure
- Algorithm
- Features of the Method
- Numerical Results
- Particle Swarm Optimization
- Computational Implementation of PSO
- Improvement to the Particle Swarm Optimization Method
- Solution of the Constrained Optimization Problem
- Ant Colony Optimization
- Basic Concept
- Ant Searching Behavior
- Path Retracing and Pheromone Updating
- Pheromone Trail Evaporation
- Algorithm
- Optimization of Fuzzy Systems
- Fuzzy Set Theory
- Optimization of Fuzzy Systems
- Computational Procedure
- Numerical Results
- Neural-Network-Based Optimization
- Practical Aspects of Optimization
- Reduction of Size of an Optimization Problem
- Reduced Basis Technique
- Design Variable Linking Technique
- Fast Reanalysis Techniques
- Incremental Response Approach
- Basis Vector Approach
- Derivatives of Static Displacements and Stresses
- Derivatives of Eigenvalues and Eigenvectors
- Derivatives of λi
- Derivatives of Yi
- Derivatives of Transient Response
- Sensitivity of Optimum Solution to Problem Parameters
- Sensitivity Equations Using Kuhn–Tucker Conditions
- Sensitivity Equations Using the Concept of Feasible Direction
- Multilevel Optimization
- Basic Idea
- Method
- Parallel Processing
- Multiobjective Optimization
- Utility Function Method
- Inverted Utility Function Method
- Global Criterion Method
- Bounded Objective Function Method
- Lexicographic Method
- Goal Programming Method
- Goal Attainment Method
- Solution of Multiobjective Problems Using MATLAB