Meeting times: 10:30-11:20 MWF

Meeting place: 213 MLH

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

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday and Wednesday 2:30-4:00. I may 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_07.html. Students are responsible for checking regularly this course web page.

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

• An Introduction to Optimization by Edwin K. P. Chong and Stanislaw H. Zak, 2nd Edition (Hardcover), Wiley-Interscience, 2001, 496 pages, ISBN: 0471391263.
• Numerical optimization by Jorge Nocedal and Stephen Wright, Springer, New York, Springer Series in Operations Research and Financial Engineering, 2006, Second edition, 664 pages, ISBN: 0387303030, (MATH Course Reserve QA402.5 .N62 1999).
• 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).
• Numerical Optimization: Theoretical and Practical Aspects by J. Frederic Bonnans, Jean Charles Gilbert, Claude Lemarechal, Claudia A. Sagastizbal Springer Series: Universitext, 2006, Second edition, 490 pages, ISBN-10: 3-540-35445-X, ISBN-13: 978-3-540-35445-1.

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 and MLH 301. Check the laboratories reservation schedule for more information. Both Fortran and Matlab are available on the network.

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 will account for 30% of the course grade.
2. The final examination will account for 35% of the course grade.
3. Homework and project assignments will account for 35% 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 85% 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.

Grader: Ricardo Ortiz-Rosado, 1K MLH, 335-0780, e-mail: rortizro@math.uiowa.edu.

Final examination: To be held on Tuesday, May 8, 12:00 noon-2:00 PM in room 213 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:
• Steepest-descent method;
• Newton-like methods;
• Quasi-Newton methods;
• Linear/nonlinear conjugate gradient methods;
• Interval reduction methods;
• Line-search methods;
• Trust-region methods;
• Local and global convergence;
2. Nonlinear equations:
• Newton's method;
• Modified Newton's methods;
• Broyden's (quasi-Newton) method;
• Inexact Newton methods;
• The bisection method;
• Line-search methods and merit functions;
• Trust-region methods;
• Local and global convergence;
3. Constrained optimization:
• Lagrange multipliers;
• Karush-Kuhn-Tucker conditions;
• Line-search methods and merit functions;
• Active-set methods (for inequality constraints);
• Penalty function methods (for equality constraints);
• Reduced-gradient and gradient-projection methods;
• Augmented Lagrangian and projected Lagrangian methods;
• Barrier methods (for inequality constraints);
• Interior-point methods (for inequality constraints);
• Sequential linearly constrained programming;
• Sequential quadratic programming;
4. More topics in optimization:
• Convexity;
• Linear programming and the simplex method;
• Quadratic programming;
• Duality;
• Nonlinear least-squares problems;
• Variational calculus;
• Nonsmooth optimization;
• Dynamic optimization and the maximum principle of Pontryagin;
• Dynamic programming and the Hamilton-Jacobi-Bellman equation;
• Neural networks and the backpropagation algorithm;
• Stochastic optimization;
• Simulated annealing;
• Genetic algorithms;

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 would like to hear from anyone who has a disability which may require seating modifications or testing accommodations or accomodations of other class requirements, so that appropriate arrangements may be made. Please contact me during my office hours.

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. Procedures for student complaints and the collegiate policy on plagiarism and cheating can be found at "Student Rights and Responsibilities" and the "College's Student Academic Handbook". All students in the College have specific rights and responsibilities. You have the right to adjudication of any complaints you have about classroom activities or instructor actions. Information is available in the College's Student Academic Handbook (http://www.clas.uiowa.edu/students/academic_handbook/). You also have the right to expect a classroom environment that enables you to learn, including modifications if you have a disability. Your responsibilities to this class and to your education as a whole-include attendance and participation. You are also expected to be honest and honorable in your fulfillment of assignments and in test-taking situations (the College's policy on plagiarism and cheating is on-line in the College's Student Academic Handbook, at http://www.clas.uiowa.edu/students/academic_handbook/). You have a responsibility to the rest of the class-and to the instructor-to help create a classroom environment where all may learn. At the most basic level, this means that you will respect the other members of the class and the instructor, and treat them with the courtesy you hope to receive in turn. Cell phones and pagers must be on silent mode during lecture and they are not allowed in class during exams. If you do bring a cell phone or pager to an exam, you may leave it in the front of the class during the exam. If a student is found to have a cell phone or pager during an exam, the cell phone or pager will be taken from the student and procedures for cheating may be followed.

Procedure for Student Complaints (and Compliments?): If you have any complaints or concerns about this course, I ask that you discuss them with me. If we cannot resolve the matter to your satisfaction and you wish to take the matter further, you may contact the Chair of the Mathematics Department in 14 MLH. Complaints should be brought to the attention of the instructor, department, and, if necessary, the associate dean, as soon as possible. Only in extraordinary cases may a complaint procedure begin six months after the time of the incident. For a full description of this policy see the "College's Student Academic Handbook".

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.