This module introduces Gradient Search Procedures, with examples and applications. Students are introduced to the use of computational algorithms, basic optimization theory, and how to find successive approximations to extreme points.
Table of Contents:
1. INTRODUCTION
2. GRADIENT SEARCH PROCEDURE
3. A CLOSER LOOK AT GRADIENT SEARCH
3.1 The Objective Function Must Decrease
3.2 The Directions of Successive Gradients
4. EXAMPLES OF THE GRADIENT SEARCH PROCEDURE
4.1 A Function Whose Level Curves are Ellipses
4.2 The Gradient Corridor
4.3 An Example Possessing Circular Level Curves
5. SPEEDING THINGS UP!
6. A MORE COMPLICATED OBJECTIVE FUNCTION AND SOME PRACTICAL ADVICE
6.1 The Importance of a Good Start
6.2 Slow Convergence: Discussion
6.3 Other Considerations
7. CONCLUDING REMARKS
8. REFERENCES
9. OPTIONAL ADDITIONAL EXERCISES
10. SPECIFIC APPLICATIONS
11. MODEL EXAM
12. HINTS AND ANSWERS TO EXERCISES
13. ANSWERS TO MODEL EXAM
ACKNOWLEDGMENT
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