22M:174/22C:174
Optimization Techniques
Spring 2005

This course will cover theory and (computational) practice for dealing with optimization problems with continuous (rather than discrete) variables, with and without constraints. These problems have immense practical significance in engineering design, management practice, and economics.

Contact/class information

Instructor:	Dr. David Stewart
Phone:	335-3832
Email:	dstewart at math<dot>uiowa<dot>edu
WWW URL:	http://www.math.uiowa.edu/~dstewart/
Office hours:	To be announced
Class times:	11:30am-12:20pm MWF
Class location:	105 MLH

You can see me outside the office hours provided it is mutually convenient.

This course will use ICON; go to http://icon.uiowa.edu/ and log in with your HawkID and password.

Textbook

Numerical Optimization by S. Wright and J. Nocedal, which is published by Springer.

Syllabus

• Unconstrained optimization theory
• Convex functions and convex sets
• Algorithms for unconstrained optimization
  • Steepest descent
  • Newton methods
  • Conjugate gradient methods
• Constrained optimization theory (Kuhn-Tucker conditions)
• Special problems:
  • Linear programming
  • Quadratic programming
• Algorithms for constrained optimization

If there is time I will start looking at dynamic optimization problems and optimal control.

Assessment

There will be one exam (30%), some sets of homework (40% total) (some of which may involve programming), and a programming assignment (30%).

Notes on programming and writing reports

Since this is a course on optimization techniques you will need to be able to program. I recommend MATLAB^TM, and I will give examples and codes in MATLAB. But you are free to use almost any other language (e.g., Fortran, C/C++, Java, Pascal). If you have another language in mind, please just check with me.

You will also need to write documentation and reports on your work and code. When you write a code, as well as including reasonable documentation in the code, you should provide at least a short statement about what it does and how to use it (and any limitations/bugs/preconditions that it has). Where appropriate, you may also need to describe how and why it works. In this documentation and in any report writing you will have to write English, and not just mathematics! You should aim to write documentation and reports that could be readily understood by someone technically literate in mathematics, computer science, physics, economics, or engineering who knows nothing about this particular course, but has an optimization problem.

Additional Notes

1. The course plan may be modified during the semester. Such modifications will be announced in advance during class periods; the student has responsibility for keeping up with such changes. You should also make a habit of reviewing the class web page, which is accessible via: 
   http://www.math.uiowa.edu/~dstewart/classes/ 
   This page will have homework details and other information posted to it as the class progresses.
2. The Department of Mathematics offices are in 14 McLean Hall (MLH). You can contact the chair of the department through the Departmental Secretary at 14 MLH or by calling 335-0714.
3. Please let you instructor know if you have a disability that requires special arrangements. I need to hear from anyone who has a disability which may require some modification of seating, testing or other class requirements so that appropriate arrangements can be made. Please see me after class or during my office hours.
4. Be sure to read the section titled Student Complaints Concerning Faculty Actions in the Schedule of Classes.
5. This course is given by the College of Liberal Arts and Sciences. This means that class policies on matters such as requirements, grading, and sanctions for academic dishonesty are governed by the College of Liberal Arts and Sciences. Students wishing to add or drop this course after the official deadline must receive the approval of the Dean of the College of Liberal Arts and Sciences. Details of the University policy of cross enrollments may be found at:

   http://www.uiowa.edu/~provost/deos/crossenroll.doc .

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