TF 12.0–1.50 Carnegie 112. Fall 2009

Course Outline

I intend to follow this outline fairly closely, but, if appropriate, I will alter what is included in the course.

Convex sets and functions: (3 weeks)
Including: separation theorems, optimality conditions.
Linear programming: (1 week)
Including: Duality and complementary slackness.
Optimality conditions in nonlinear programming: (2 weeks)
Including: Fritz John conditions, Karush-Kuhn-Tucker conditions.
Duality in nonlinear programming: (2 weeks)
Including: Lagrangian duality, saddle points.
Nonlinear programming algorithms: (6 weeks)
Including: Steepest descent, Newton’s method, penalty and barrier methods, SQP methods.

Homework: Approximately every two weeks. You should learn a fair amount from the homeworks. Therefore, try working out the solutions on your own. If you have difficulties, you may talk to me or to other students about the homeworks, but you must write up your solutions on your own. You may be able to find the solutions to some of the homework and exam questions on the web: do not use these solutions!

Exams: One takehome midterm, one in class final (scheduled for the last day of classes). The midterm will cover items 1–4 from the list of topics above.

Grades: Homeworks and the two exams will each count for one third of the grade.

Office Hours: Tuesday, 2.0–3.0PM and Wednesday 11am-12noon, in Amos Eaton 325.

Attendance: Strongly encouraged. Active engagement in class will greatly help you in understanding the material.

Textbooks:

Required:	Bazaraa, Sherali and Shetty, Nonlinear Programming: Theory and Algorithms. Wiley, 1993.
		I will follow this book fairly closely.
On Reserve:	Rockafellar, Convex Analysis. Princeton 1970.
		Convex analysis bible.
	Ruszczynski, Nonlinear Optimization. Princeton University Press, 2006.
		I’ve previously used this text for this course. It contains more material on nonsmooth optimization.
	Luenberger, Introduction to Linear and Nonlinear Programming. Addison-Wesley, 1984.
	Mangasarian, Nonlinear Programming. McGraw-Hill, 1969.
		A classic text reprinted by SIAM.
	Nash and Sofer, Linear and Nonlinear Programming. McGraw-Hill, 1996.
		Ruszczynski, Luenberger, Mangasarian, and Nash & Sofer are good alternatives to Bazaraa et al.
	Nocedal and Wright, Numerical Optimization. Springer, 1999.
		A good recent text, with an emphasis on algorithms.
	Fletcher, Practical Methods of Optimization. Wiley, 1987.
		Concentrates more on methods of nonlinear programming.

The World Wide Web: This outline and the homeworks will be available via my homepage,

http://www.rpi.edu/~mitchj/matp6600

Student learning objectives: Develop a thorough understanding of the theory and algorithms of nonlinear programming.

Cell phones: Please make sure that cell phones and pagers are turned off during class.

Academic integrity: Student-teacher relationships are based on mutual trust. Acts which violate this trust undermine the educational process. The Rensselaer Handbook defines various forms of academic dishonesty and procedures for responding to them. The penalties for cheating can include failure in the course, as well as harsher punishments.

John Mitchell

Amos Eaton 325

276–6915.

mitchj at rpi dot edu