OPTIMIZATION TECHNIQUES-22M:174/22C:174

SPRING SEMESTER 2003


SYLLABUS

Meeting times: 8:30-9:20 MWF

Meeting place: 221 MLH

Prerequisites: 22M:100 or equivalent. A knowledge of computer programming.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: 9:30-10:20 MWF. I will also be available at other times. Just drop by my office or send me an e-mail to make an appointment.

Telephone: (319)-335-0898

Fax: (319)-335-0627

E-mail address: ljay@math.uiowa.edu

Mailbox: in Mailroom 15 MLH

Course web page: Assignments and other information about the course will be given in http://www.math.uiowa.edu/~ljay/m174_03.html. Students are responsible for checking regularly this course web page.

Textbook (reference): Numerical optimization by Jorge Nocedal and Stephen Wright, Springer, New York, Springer Series in Operations Research, 1999, Second Printing, 664 pages, ISBN: 0-387-98793-2, Price: $69.95, (MATH Course Reserve QA402.5 .N62 1999 ).

My own classnotes based on diverse sources will be available to students. Additional recommended references are:

Nonlinear programming by Dimitri P. Bertsekas, Athena Scientific, Belmont, MA, 1995, ISBN 1-886529-14-0, (MATH Course Reserve T 57.8 .B477 1995).
Numerical methods for unconstrained optimization and nonlinear equations by John E. Dennis and Robert B. Schnabel, Prentice Hall, Englewood Cliffs, NJ, 1988, reprinted by SIAM publications, 1993, ISBN 0-89871-364-1, (MATH Course Reserve QA402.5 .D44 1983).
Practical methods of optimization by R. Fletcher, Second edition, John Wiley & Sons, Chichester, New-York, 1987, ISBN 0-471-91547-5, (ENGINEERING QA402.5 .F43 1987).
Practical optimization by Philip E. Gill, Walter Murray and Margaret H. Wright, Academic Press, New York, NY, 1981, ISBN 0-12-283950-1 (ENGINEERING QA402.5 G54).
Linear and nonlinear programming by David G. Luenberger, second edition, Addison-Wesley Publ. Comp., Reading, MA, 1984, ISBN 0-201-15794-2, (MATH Course Reserve T 57.7 .L8 1984).

Goals and objectives of the course: This course is a graduate course and it is assumed that you can work along the course in an independent fashion. This course will cover modern optimization techniques for both constrained and unconstrained optimization with continuous (as opposed to discrete) variables. Given its strong links to optimization techniques, the numerical solution of nonlinear equations will also be considered. At the end of the course the student should master most of the issues in numerical optimization.

Class procedures: The majority of each class period will be lecture oriented. It is strongly advised to read the material to be discussed before coming to class. I will generally hand out in advance the notes related to the material to be covered during the next class(es).

Computer languages: The predominant programming languages used in numerical analysis are Fortran and Matlab. For programming assignments, other languages will be accepted; but no programming assistance will be given for such languages (e.g., Maple, Mathematica, Pascal, C, C++, and Java).

Computer resources: Computer accounts will be made available on the network in MLH B5. Check the laboratories reservation schedule and the web page of the Division of Mathematics Sciences Educational Laboratories for more information. Both Fortran and Matlab are available on the network in MLH 301.

Grading procedures: The final grade will be based on one mid-term examination, the final examination, and homework, as follows:

  1. The mid-term examination and the final examination will each account for 30% of the course grade.
  2. Homework and project assignments will account for 40% of the course grade. Late homework will be accepted only by special permission of the instructor. The grade for your homework will be based on the best 75% of your homework.

The tests are open books and open notes examinations. Bring a scientific calculator. In assigning grades, plus/minus grading will be used.

Teaching assistant: Kristen Sellke, 255MH, 335-0654, e-mail: ksellke@math.uiowa.edu.

Final examination: To be held on Thursday, May 15, 12:00 noon-2:00 PM in room 221 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination. This final examination is an open books and open notes examination. Bring a scientific calculator.

Course outline: We will cover as many topics as possible, but of course several of them will be skipped due to time limits. Characterization of solutions (such as optimality conditions in optimization) and convergence analysis of the algorithms will be essential to this course. We give below a partial list of topics and algorithms to be treated in connexion with three general classes of problems:

  1. Unconstrained optimization:
  2. Nonlinear equations:
  3. Constrained optimization:
  4. More topics in optimization:

This course plan may be modified during the semester. Such modifications will be announced in advance during class periods and on the course web page; the student is responsible for keeping abreast of such changes.

Notes to student: The Department of Mathematics has offices in 14 MLH. To make an appointment to speak with the Chair of the Department, call 335-0714 or contact the Departmental Secretary in 14 MLH.

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 may be made. Please see me after class or during my office hours.