ESE504-402 : Introduction to Optimization Theory

	ESE 504-402 : Introduction to Optimization Theory Department of Electrical and Systems Engineering University of Pennsylvania
	Fall 2009

Announcements :
Midterm Exam on Tuesday November 17th at 4:30pm in class. You can bring one letter size "cheat sheet" with you.
First class is on September 15 at 4:30pm in Towne Building, Room 313.

Course Description: This course deals with the mathematical theory of optimization. Topics covered include

Linear programming, Simplex method, duality theory, theorems of alternative.
Network flow problems, elements of integer programming.
Nonlinear programming, Karush Kuhn Tucker conditions.
A brief overview of interior point methods and global optimization techniques.

Requirement: Familiarity with linear algebra is required. Undergraduates need permission.

Instructor:

Ali Jadbabaie , jadbabai@seas.upenn.edu ,
Office hours : Wednesdays 3:00-5:00pm or by appointment, 365 GRW Moore bldg

Lectures: Tuesdays 4:30pm-7:30pm in Towne 313

Recommended Text
- Introduction to Linear Optimization, by D. Bertsimas and J. N. Tsitsiklis
Other References
- D. G. Luenberger, Linear and Nonlinear Programing. Addison-Wesley, 1984.
- W. L. Winston, Introduction to Mathematical Programing Duxbury Press, Second Edition, 1995.
- R. Vanderbei, Linear Programing: Foundations and Extensions Princeton University Press
Grading:
- Homeworks : 20%
- Midterm : 35%
- Final : 45%
Teaching assistant:
Homework sets:

here

Linear Algebra Notes and Resources :
These notes contains the minimum amount of linear algebra that is required for this course.
Historical References

Biography of George Dantzig inventor of the Simplex method of linear programing problems.

Biography of Leonid Vitaliyevich Kantorovich, Father of linear programing and co-winner of
the 1975 Nobel prize in economics, "for contributions to the theory of optimum allocation of resources".

Other Resources

Slides of Professor Dimitri Bertsimas from MIT Open courseware

Tentative Weekly Schedule (please note that the recommended text is just a reference, we will not follow it exactly):

Date Lecture/Week Reading Contents

September 9 Lecture 1 Chapters 1, 2 Introduction to optimization, Linear Programing Problem formulation, examples

September 14 Lecture 2 Notes Linear Algebra review

September 21 Lecture 3 Chapter 2 Review of Convex sets/Linear Algebra

September 28 Lecture 4 Chapter 2,3 Geometry of LP/The Simplex Method

October 5 Lecture 5 Chapter 3 Simpelx Method

October 12 Lecture 6 Chapters 3,4 Fundamental insights/duality

October 19 Lecture 8 Chapter 4,5 More on Duality Theory/Sensitivity

October 26 Lecture 9 Network Flow/Transportation Chapter 6

November 2 Lecture 10 Chapter 10 Integer Programing

November 9 Lecture 11 midterm midterm

November 16 Lecture 12 notes and slides, Chapter 11 Combinatorial Optimization

November 23 Lecture 13 notes and slides Nonlinear Optimization

November 30 Lecture 13 More on Nonlinear Optimization/Review/Final Given Notes/

December 7/td> Lecture 13 More on Nonlinear Optimization/Review/Final Given Notes/

Date	Lecture/Week	Reading	Contents
September 9	Lecture 1	Chapters 1, 2	Introduction to optimization, Linear Programing Problem formulation, examples
September 14	Lecture 2	Notes	Linear Algebra review
September 21	Lecture 3	Chapter 2	Review of Convex sets/Linear Algebra
September 28	Lecture 4	Chapter 2,3	Geometry of LP/The Simplex Method
October 5	Lecture 5	Chapter 3	Simpelx Method
October 12	Lecture 6	Chapters 3,4	Fundamental insights/duality
October 19	Lecture 8	Chapter 4,5	More on Duality Theory/Sensitivity
October 26	Lecture 9	Network Flow/Transportation	Chapter 6
November 2	Lecture 10	Chapter 10	Integer Programing
November 9	Lecture 11	midterm	midterm
November 16	Lecture 12	notes and slides, Chapter 11	Combinatorial Optimization
November 23	Lecture 13	notes and slides	Nonlinear Optimization
November 30	Lecture 13	More on Nonlinear Optimization/Review/Final Given	Notes/
December 7/td>	Lecture 13	More on Nonlinear Optimization/Review/Final Given	Notes/

Last modified : September 8, 2009. Send comments to Ali Jadbabaie

ESE 504-402 : Introduction to Optimization Theory