IE 505
Mathematical Programming
Instructor:
M. C. Pinar
Room:
Dean's office, ext. 2603
Office Hours:
Wednesdays 15:3017:30.
Reference
Material, Textbook (partially) and Online Resources:

Optimization: Insights and Applications,
J.
Brinkhuis
and V. Tikhomirov, Princeton Univ. Press, 2005.
 Convex
Optimization, S.
Boyd
and L. Vandenberghe, Cambridge Univ. Press, 2004.
 Convex
Analysis and Optimization: Lecture Notes by
A. Nemirovski, Technion.
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 selfcontained 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:
 Introduction to calculus
and optimization for
single variable functions on R, differential calculus, Fermat Theorem, and concrete examples (2 weeks)
 Optimization of multivariate
functions, Fermat Theorem for two or more variables, concrete problems (2 weeks)
 Equality Constrained
problems, Lagrange Multipliers, examples (2 weeks)
 Inequality Constraints, KarushKuhnTucker Theory, examples (2 weeks)
 Convexity, Convex Programming, Linear
and Quadratic Programming, Lagrange Duality (2 weeks)
 Economic Applications
of Optimization: Asset selling, optimal discounts on tickets, arbitrage in financial markets. (2 weeks)
 Optimization with Integers (2 weeks)
Policy on Homework and Exams
 Your success in the course depends greatly on doing the homework
exercises on your own.
 I will upload the hw questions in MOODLE.
 Late hws will not be accepted.
 Cheating (unauthorized cooperation or lifting answers from an online or printed source without due citation) in homework and exams has serious consequences.
Therefore, all work submitted should reflect your own effort.
Grading
Homeworks: 
20 %

2 Midterm Tests: 
50 % TBA

Final: 
30 % TBA.
