Meeting times: 8:30-9:20 MWF

Meeting place: 218 MLH

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

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday 9:30AM-11:00AM and Wednesday 9:30AM-11:00AM. 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.html. Students are responsible for checking regularly this course web page.

Textbook: No particular textbook will be followed. My classnotes based on several sources will be available to students. 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).

Numerical optimization by Philip E. Gill and Margaret H. Wright, Class Notes. Selected parts will be copied and distributed with permission of the authors.

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).

Numerical optimization by Jorge Nocedal and Stephen Wright, to appear around April 1999. Selected parts will be copied and distributed with permission of the authors.

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. Mathematica, Pascal and C).

Computer resources: Computer accounts will be made available on the Hewlett-Packard Unix workstation network in MLH B5. This room will be reserved on Monday from 11:30AM until 12:30PM. Check the laboratories reservation schedule and the web page of the Division of Mathematic Sciences Educational Laboratories for more information. Both Fortran and Matlab are also available on the HP/SGI network in MLH 301, and for engineering students, they are also available on the HP workstations in ICAEN.

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.

Final examination: To be held on Wednesday, May 12, 2:15-4:15 PM in room 218 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 classes of problems:

1. Nonlinear equations:
• The bisection method
• Newton's method
• Finite difference Newton's method
• Secant methods
• Modified Newton methods
• Inexact Newton methods
• Quasi-Newton methods (Broyden's method)
2. Unconstrained optimization:
• Convexity
• Line-search methods
• Step-length selection algorithms
• Trust-region methods
• Steepest-descent methods
• Linear/Nonlinear conjugate gradient methods
• Newton-like methods
• Quasi-Newton methods
3. Constrained optimization with (in)equality constraints:
• Lagrange multipliers
• Active-set methods (for inequality constraints)
• Linear programming
• Quadratic programming
• Interior-point methods (for inequality constraints)
• Penalty function methods
• Barrier methods (for inequality constraints)
• Reduced-gradient methods
• Gradient-projection methods
• Augmented Lagrangian methods
• Projected Lagrangian methods
• Sequential linearly constrained programming
• Sequential quadratic programming
• Duality

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.

Please let your instructor know if you have a disability which requires special arrangements.