Course meeting times: 1:30-2:20 MWF. Standard out-of-class preparation is at least six hours.

Course meeting place: 214 MLH

Prerequisites: 22M:027 (MATH:2700), 22M:028 (MATH:2850) or 22M:056 (MATH:3780), and 22M:072 (MATH:3800). Some knowledge of computer programming with for example Matlab, Maple, Mathematica, Scilab, or Octave.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday and Wednesday 10:30-noon. 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_11.html. Students are responsible for checking regularly this course web page.

Goals and objectives of the course: This course is at a graduate level 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 some essential issues in numerical optimization.

Textbook:

Additional references:

• An Introduction to Optimization by Edwin K. P. Chong and Stanislaw H. Zak, 2nd Edition (Hardcover), Wiley-Interscience, 2001, 496 pages, ISBN: 0471391263.
• 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.

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.

Class procedures: The majority of each class period will be lecture oriented.

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).

Linux computer accounts: Linux computer accounts will be made available on the Linux network in MLH (computer lab rooms B5 and 301). You can also use the NoMachine NX Client Windows software to access your Linux computer account remotely. Accounts for students who are not majoring in Computer Science, Mathematics, or Statistics and Actuarial Science will be deleted after the term has ended! Note the expiration date at the top of your Unix Account Information form. The directory for this class will be removed before the beginning of the next term! If there is anything in this directory that you would like to save, you must archive it to your own home directory.

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

1. There will be 2 tests during the semester, with each test to account for 15% of the course grade.
2. The final examination will account for 45% of the course grade.
3. Homework and project assignments will account for 25% 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 all the homeworks minus your worst 2 scores.

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

Grader: Hongbo Dong, 1K MLH, 335-0780, e-mail: hongbo-dong@u@uiowa.edu.

Final examination: To be held on Wednesday, May 11 2011, 9:45-11:45 AM in room 214 MLH (7:30-9:30AM is still available for those who prefer to come early, please let me know if you want to take the final exam at that time). 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.

Add or drop: 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.

Cross enrollments: Details of the University policy of cross enrollments may be found at: http://www.uiowa.edu/~provost/deos/crossenroll.doc.

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.

The College of Liberal Arts and Sciences Policies and Procedures

Administrative Home: The College of Liberal Arts and Sciences is the administrative home of this course and governs matters such as the add/drop deadlines, the second-grade-only option, and other related issues. Different colleges may have different policies. Questions may be addressed to 120 Schaeffer Hall, or see the CLAS Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/.

Electronic Communication: University policy specifies that students are responsible for all official correspondences sent to their University of Iowa e-mail address (@uiowa.edu). Faculty and students should use this account for correspondences. (Operations Manual, III.15.2 at http://www.uiowa.edu/~our/opmanual/iii/15.htm#152/ Scroll down to k.11.)

Accommodations for Disabilities: A student seeking academic accommodations should first register with Student Disability Services and then meet privately with the course instructor to make particular arrangements. See http://www.uiowa.edu/~sds/ for more information.

Academic Fraud: Plagiarism and any other activities when students present work that is not their own are academic fraud. Academic fraud is a serious matter and is reported to the departmental DEO and to the Associate Dean for Undergraduate Programs and Curriculum. Instructors and DEOs decide on appropriate consequences at the departmental level while the Associate Dean enforces additional consequences at the collegiate level. See the CLAS Academic Fraud section of the Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/x/#2.

CLAS Final Examination Policies: Final exams may be offered only during finals week. No exams of any kind are allowed during the last week of classes. Students should not ask their instructor to reschedule a final exam since the College does not permit rescheduling of a final exam once the semester has begun. Questions should be addressed to the Associate Dean for Undergraduate Programs and Curriculum.

Making a Suggestion or a Complaint: Students with a suggestion or complaint should first visit the instructor, then the course supervisor, and then the departmental DEO. Complaints must be made within six months of the incident. See the CLAS Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/x/#5.

Understanding Sexual Harassment: Sexual harassment subverts the mission of the University and threatens the well-being of students, faculty, and staff. All members of the UI community have a responsibility to uphold this mission and to contribute to a safe environment that enhances learning. Incidents of sexual harassment should be reported immediately. See the UI Comprehensive Guide on Sexual Harassment at http://www.uiowa.edu/~eod/policies/sexual-harassment-guide/index.html for assistance, definitions, and the full University policy.

Reacting Safely to Severe Weather: In severe weather, class members should seek appropriate shelter immediately, leaving the classroom if necessary. The class will continue if possible when the event is over. For more information on Hawk Alert and the siren warning system, visit the Public Safety web site at http://www.uiowa.edu/~pubsfty/intlinks.htm.

Resources:

• Writing Center 110 English-Philosophy Building, 335-0188, http://www.uiowa.edu/~writingc
• Speaking Center 12 English-Philosophy Building, 335-0205, http://www.uiowa.edu/~rhetoric/centers/speaking
• Mathematics Tutorial Laboratory 314 MacLean Hall, 335-0810, http://www.math.uiowa.edu/MathTutorialLab/
• Tutor Referral Service Campus Information Center, Iowa Memorial Union, 335-3055, http://www.imu.uiowa.edu/cic/tutor_referral_service

Student Classroom Behavior: The ability to learn is lessened when students engage in inappropriate classroom behav- ior, distracting others; such behaviors are a violation of the Code of Student Life. When disruptive activity occurs, a University instructor has the authority to determine class- room seating patterns and to request that a student exit immediately for the remainder of the period. One-day suspensions are reported to appropriate departmental, collegiate, and Student Services personnel (Office of the Vice President for Student Services and Dean of Students).

University Examination Policies: Missed exam policy. University policy requires that students be permitted to make up examinations missed because of illness, mandatory religious obligations, certain University activities, or unavoidable circumstances. Excused absence forms are available at the Registrar web site: http://www.registrar.uiowa.edu/forms/absence.pdf

Final Examinations: An undergraduate student who has two final examinations scheduled for the same period or more than three examinations scheduled for the same day may file a request for a change of schedule before the published deadline at the Registrar's Service Center, 17 Calvin Hall, 8-4:30 M-F, (384-4300).