67.611/92.671 Mathematical Programming - Outline

• Course Outline: This course is concerned with the theory of nonlinear programming. I intend to follow this outline fairly closely, but, if appropriate, I will alter what is included in the course.
  1. Convex sets and functions: (4 weeks) Including: separation theorems, optimality conditions.
  2. Linear programming: (1 week) Including: Duality and complementary slackness.
  3. Optimality conditions in nonlinear programming: (2 weeks) Including: Fritz John conditions, Karush-Kuhn-Tucker conditions.
  4. Duality in nonlinear programming. (3 weeks) Including: Lagrangian duality, saddle points.
  5. Quadratic programming and the linear complementarity problem: (2 weeks) Including: Lemke's algorithm.
  6. Topics: (1 week) Still to be decided.
• 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.
• Exams: One in class midterm, one takehome final.
• Grades: Homeworks and the two exams will each count for one third of the grade.
• Office Hours: Monday, Wednesday 2.0--4.0.
• Textbooks:

  Required:	Bazaraa, Sherali and Shetty, Nonlinear Programming: Theory and Algorithms. Wiley, 1993.
  	I will follow (the first six chapters of) this book fairly closely.
  On Reserve:	Rockafellar, Convex Analysis. Princeton 1970.
  	Convex analysis bible.
  	Luenberger, Introduction to Linear and Nonlinear Programming. Addison-Wesley, 1984.
  	Mangasarian, Nonlinear Programming. McGraw-Hill, 1969.
  	Luenberger and Mangasarian are both good alternatives to Bazaraa, Sherali and Shetty.
  	Fletcher, Practical Methods of Optimization. Wiley, 1987.
  	Concentrates more on methods of nonlinear programming.

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