# Unconstrained Optimization (UMAP)

### Author: Joan R. Hundhausen and Robert A. Walsh

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. INTRODUCTION2. GRADIENT SEARCH PROCEDURE3. 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. A MORE COMPLICATED OBJECTIVE FUNCTION AND SOME PRACTICAL ADVICE

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

8. REFERENCES

9. OPTIONAL ADDITIONAL EXERCISES

10. SPECIFIC APPLICATIONS

11. MODEL EXAM

12. HINTS AND ANSWERS TO EXERCISES

13. ANSWERS TO MODEL EXAM

ACKNOWLEDGMENT

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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