IE 505 Mathematical Programming

Instructor: M. C. Pinar
Room: 305, ext. 1514
Office Hours: TBA.

Reference Material, Textbooks and Online Resources:

   The material listed above is for students' reference. The course will be based on the instructor's notes. 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.

  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 (2 weeks)
  6.    Economic Applications of Optimization: Asset selling, optimal discounts on tickets, arbitrage in financial markets, martingales, Nash bargaining, second welfare theorem of mathematical economics, etc.. (2 weeks)
  7.    Mathematical Applications of Optimization: Matrices, linear inequalities, the problem of Apollonius, Quadratics, polynomials of least deviation etc.. (2 weeks)

Policy on Homework and Exams



Homeworks: 30 %

Midterm Test: 30 % TBA
Final: 40 % TBA.