IE 505 Mathematical Programming

Instructor: M. C. Pinar
Room: Dean's office, ext. 2603
Office Hours: Tuesdays and Thursdays open door.

Reference Material, Textbook (partially) and Online Resources:

   The material listed above is for students' reference. The course will be based on the instructor's notes. We shall follow, in compressed form, the textbook by Brinkhuis and Tikhomirov during the first half of the course. The course will make a self-contained introduction to the basics of optimization in finite dimensions with emphasis on modeling and optimality conditions geared towards a practical problem solving approach. No previous background in optimization is assumed. The instructor will provide his own lecture notes in MOODLE. The homework questions will be selected from applications in economics, finance, electrical engineering and the like. We shall also use the Maple symbolic package throughout the course.

  Course Contents:
  1.    Introduction to calculus and optimization for single variable functions on R, differential calculus, Fermat Theorem, and concrete examples (2 weeks)
  2.    Optimization of multivariate functions, Fermat Theorem for two or more variables, concrete problems (2 weeks)
  3.    Equality Constrained problems, Lagrange Multipliers, examples (2 weeks)
  4.    Inequality Constraints, Karush-Kuhn-Tucker Theory, examples (2 weeks)
  5.    Convexity, Convex Programming, Linear and Quadratic Programming, Lagrange Duality (2 weeks)
  6.    Economic Applications of Optimization: Asset selling, optimal discounts on tickets, arbitrage in financial markets. (2 weeks)
  7.    Optimization with Integers (2 weeks)

Policy on Homework and Exams



Homeworks: 20 %

1 Midterm Test: 40 % TBA
Final: 40 % TBA.