ESE504-402 : Introduction to Optimization Theory

	ESE 504-402 : Introduction to Optimization Theory Department of Electrical and Systems Engineering University of Pennsylvania
	Fall 2006

Announcements :
- First class is on September 12 at 4:30pm in 313 Towne.
Course Description: This course deals with the mathematical theory of optimization. Topics covered include
- Linear programming, Simplex method, duality theory.
- 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 introductory linear algebra is required.
Instructor:
- Ali Jadbabaie , jadbabai@seas.upenn.edu ,
  Office hours : Thursdays 2:00-4:00pm, 365 GRW Moore bldg
Lectures: Tuesdays 4:30pm-7:30pm, 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.

Grading:

Homeworks : 30%

Midterm : 30%

Final : 40%

Teaching assistant:

Ali Ahmadzadeh aliahmad@grasp.upenn.edu.Office hours:TBA.

Homework sets:

Most homework problems are either from the text or from Professor Lieven Vandenberghe's homework set which can be found here .

Homework 1: Problems 1.8, 1.9, 1.12 from the textbook. Exercises 4 (a,e), 7,9,10 from homework set. Due on Tuesday September 26th in class.

Linear Algebra Notes:

A Tutorial on Linear Algebra by Professor C. T. Abdallah

Linear Algebra Review by Professor Fernando Paganini, UCLA.

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Historical References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

Throught the course we will use the following resources.

Slides of Professor Dimitri Bertsimas from MIT Open courseware

Professor Lieven Vandenberghe's lecture notes from UCLA

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

Date Lecture Reading Contents

September 12 Lecture 1 Chapters 1, 2 Introduction to optimization, Linear Programing Problem formulation, examples

September 19 Lecture 2 Chapter 2 Geometry of LP, Some Linear Algebra/Convexity

September 26 Lecture 3 Chapter 2 Review of Convex sets/Linear Algebra

October 3 Lecture 4 Chapter 3 The Simplex Method

October 10 Lecture 5 Chapter 1,2,3/notes Examples/Review

October 17 Lecture 6 Chapters 3,4 Fundamental insights/duality

October 24 Fall Break Fall Breal Fall Break

October 31 Lecture 8 Chapter 4,5 More on Duality Theory/Sensitivity

November 7 Lecture 9 Midterm in class Midterm

November 13 Lecture 10 Chapter 6 Network flow/Transportation Problems

November 20 Lecture 11 CHapter 10 Integer Programing

November 27 Lecture 12 notes and slides nonlinear programing

December 5 Lecture 13 Take-home final Final Exam

Date	Lecture	Reading	Contents
September 12	Lecture 1	Chapters 1, 2	Introduction to optimization, Linear Programing Problem formulation, examples
September 19	Lecture 2	Chapter 2	Geometry of LP, Some Linear Algebra/Convexity
September 26	Lecture 3	Chapter 2	Review of Convex sets/Linear Algebra
October 3	Lecture 4	Chapter 3	The Simplex Method
October 10	Lecture 5	Chapter 1,2,3/notes	Examples/Review
October 17	Lecture 6	Chapters 3,4	Fundamental insights/duality
October 24	Fall Break	Fall Breal	Fall Break
October 31	Lecture 8	Chapter 4,5	More on Duality Theory/Sensitivity
November 7	Lecture 9	Midterm in class	Midterm
November 13	Lecture 10	Chapter 6	Network flow/Transportation Problems
November 20	Lecture 11	CHapter 10	Integer Programing
November 27	Lecture 12	notes and slides	nonlinear programing
December 5	Lecture 13	Take-home final	Final Exam

Last modified : September 7, 2006. Send comments to Ali Jadbabaie

ESE 504-402 : Introduction to Optimization Theory