Applied Optimization With Matlab Programming Book

PREFACE.

1 Introduction.

1.1 Optimization Fundamentals.

1.1.1 Elements of Problem Formulation.

1.1.2 Mathematical Modeling.

1.1.3 Nature of Solution.

1.1.4 Characteristics of the Search Procedure.

1.2 Introduction to MATLAB.

1.2.1 Why MATLAB?

1.2.2 MATLAB Installation Issues.

1.2.3 Using MATLAB the First Time.

1.2.4 Using the Editor.

1.2.5 Creating a Code Snippet.

1.2.6 Creating a Program.

Problems.

2 Graphical Optimization.

2.1 Problem Definition.

2.1.1 Example 2.1.

2.1.2 Format for the Graphical Display.

2.2 Graphical Solution.

2.2.1 MATLAB High-Level Graphics Functions.

2.2.2 Example 2.1 Graphical Solution.

2.2.3 Displaying the Graphics.

2.2.4 Customizing the Figure.

2.3 Additional Examples.

2.3.1 Example 2.2.

2.3.2 Example 2.3.

2.3.3 Example 2.4.

2.4 Additional MATLAB Graphics.

2.4.1 Handle Graphics.

2.4.2 Graphical User Interface.

2.4.3 GUI Code.

References.

Problems.

3 Linear Programming.

3.1 Problem Definition.

3.1.1 Standard Format.

3.1.2 Modeling Issues.

3.2 Graphical Solution.

3.2.1 Example 3.1.

3.2.2 Characteristics of the Solution.

3.2.3 Different Solution Types.

3.3 Numerical Solution the Simplex Method.

3.3.1 Features of the Simplex Method.

3.3.2 Application of Simplex Method.

3.3.3 Solution Using MATLAB.

3.3.4 Solution Using MATLAB s Optimization Toolbox.

3.4 Additional Examples.

3.4.1 Example 3.2 Transportation Problem.

3.4.2 Example 3.3 Equality Constraints and Unrestricted Variables.

3.4.3 Example 3.4 A Four-Variable Problem.

3.5 Additional Topics in LinearProgramming.

3.5.1 Primal and Dual Problem.

3.5.2 Sensitivity Analysis.

References.

Problems.

4 Nonlinear Programming.

4.1 Problem Definition.

4.1.1 Problem Formulation Example 4.1.

4.1.2 Discussion of Constraints.

4.2 Mathematical Concepts.

4.2.1 Symbolic Computation Using MATLAB.

4.2.2 Basic Mathematical Concepts.

4.2.3 Taylor s Theorem/Series.

4.3 Graphical Solutions.

4.3.1 Unconstrained Problem.

4.3.2 Equality Constrained Problem.

4.3.3 Inequality Constrained Problem.

4.3.4 Equality and Inequality Constraints.

4.4 Analytical Conditions.

4.4.1 Unconstrained Problem.

4.4.2 Equality Constrained Problem.

4.4.3 Inequality Constrained Optimization.

4.4.4 General Optimization Problem.

4.5 Examples.

4.5.1 Example 4.2.

4.5.2 Example 4.3.

References.

Problems.

5 Numerical TechniquesThe One-Dimensional Problem.

5.1 Problem Definition.

5.1.1 Constrained One-Dimensional Problem.

5.2 Solution to the Problem.

5.2.1 Graphical Solution.

5.2.2 Newton-Raphson Technique.

5.2.3 Bisection Technique.

5.2.4 Polynomial Approximation.

5.2.5 Golden Section Method.

5.3 Importance of the One-Dimensional Problem.

5.4 Additional Examples.

5.4.1 Example 5.2 Illustration of General Golden Section Method.

5.4.2 Example 5.3 Two-Point Boundary Value Problem.

5.4.3 Example 5.4 Root Finding with Golden Section.

References.

Problems.

6 Numerical Techniques for Unconstrained Optimization.

6.1 Problem Definition.

6.1.1 Example 6.1.

6.1.2 Necessary and Sufficient Conditions.

6.1.3 Elements of a Numerical Technique.

6.2 Numerical Techniques Nongradient Methods.

6.2.1 Random Walk.

6.2.2 Pattern Search.

6.2.3 Powell s Method.

6.3 Numerical Techniques Gradient-Based Methods.

6.3.1 Steepest Descent Method.

6.3.2 Conjugate Gradient (Fletcher-Reeves)Method.

6.3.3 Davidon-Fletcher-Powell Method.

6.3.4 Broydon-Fletcher-Goldfarb-Shanno Method.

6.4 Numerical Techniques Second Order.

6.5 Additional Examples.

6.5.1 Example 6.2 Rosenbrock Problem.

6.5.2 Example 6.3 Three-Dimensional Flow near a Rotating Disk.

6.5.3 Example 6.4 Fitting Bezier Parametric Curves.

References.

Problems.

7 Numerical Techniques for Constrained Optimization.

7.1 Problem Definition.

7.1.1 Problem Formulation Example 7.1.

7.1.2 Necessary Conditions.

7.1.3 Elements of a Numerical Technique.

7.2 Indirect Methods for Constrained Optimization.

7.2.1 Exterior Penalty Function (EPF)Method.

7.2.2 Augmented Lagrange Multiplier (ALM)Method.

7.3 Direct Methods for Constrained Optimization.

7.3.1 Sequential Linear Programming (SLP).

7.3.2 Sequential Quadratic Programming (SQP).

7.3.3 Generalized Reduced Gradient (GRG)Method.

7.3.4 Sequential Gradient Restoration Algorithm (SGRA).

7.4 Additional Examples.

7.4.1 Example 7.2 Flagpole Problem.

7.4.2 Example 7.3 Beam Design.

7.4.3 Example 7.4 Optimal Control.

References.

Problems.

8 Discrete Optimization.

8.1 Concepts in Discrete Programming.

8.1.1 Problem Relaxation.

8.1.2 Discrete Optimal Solution.

8.2 Discrete Optimization Techniques.

8.2.1 Exhaustive Enumeration.

8.2.2 Branch and Bound.

8.2.3 Dynamic Programming.

8.3 Additional Examples.

8.3.1 Example 8.4 I Beam Design.

8.3.2 Zero One Integer Programming.

References.

Problems.

9 Global Optimization.

9.1 Problem Definition.

9.1.1 Global Minimum.

9.1.2 Nature of the Solution.

9.1.3 Elements of a Numerical Technique.

9.2 Numerical Techniques and Additional Examples.

9.2.1 Simulated Annealing (SA).

9.2.2 Genetic Algorithm (GA).

References.

Problems.

10 Optimization Toolbox from MATLAB.

10.1 The Optimization Toolbox.

10.1.1 Programs.

10.1.2 Using Programs.

10.1.3 Setting Optimization Parameters.

10.2 Examples.

10.2.1 Linear Programming.

10.2.2 Quadratic Programming.

10.2.3 Unconstrained Optimization.

10.2.4 Constrained Optimization.

Reference.

Index.