ESE605 : Modern Convex Optimization

	ESE 605: Modern Convex Optimization Department of Electrical and Systems Engineering University of Pennsylvania
	Spring 2008

Announcements :
- First class is on January 17 at 3:00pm in Towne 309.
Course Description: This course deals with theory, applications and algorithms of convex optimization, based on advances in interior point methods for convex programing. The course is divided in 3 parts: Theory, applications, and algorithms. The theory part covers basics of convex analysis and convex optimization problems such as linear programing (LP), semidefinite programing (SDP), second order cone programing (SOCP), and geometric programing (GP), as well as duality in general convex and conic optimization problems. In the next part of the course, we will focus on engineering applications of convex optimization, from systems and control theory to estimation, data fitting, information theory, statistics and machine learning. Finally, in the last part of the course we discuss the details of interior point algorithms of convex programing as well as their compelxity analysis.
Requirement: This course is math intensive. A solid working knowledge of linear algebra, analysis, probability and statistics is required. Undergraduates need permission.
Instructor:
- Ali Jadbabaie , jadbabai (at) seas (dot) upenn (dot) edu ,
  Office hours : Wednesdays from 2:00-4:00pm or by appointment, 365 GRW Moore bldg
Lectures: Tuesdays and Thursdays 3:00pm-4:30pm in Towne 309

Required Text
- S. P Boyd and L. Vandenberghe, Convex Optimization
Other References
- J. Renegar, A Mathematical View of Interior Point Methods for Convex Optimization
- A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, SIAM, 2001
- D. Bertsekas, A. Nedic, and A Ozdaglar, Convex Analysis and Optimization , 2003.
Grading:
- Homework : 30%
- Midterm : 30%
- Final : 40%
Teaching assistant:
- Alireza Tahbaz-Salehi, and Kayhan Batmanghelich . Office hours TBD.
Homework sets:
Other resources:

Professor Stephen Boyd's lectures at Stanford.
Professor Gilbert Strang's Linear Algebra lectures at MIT.

Software:
- CVX A Matlab-based software for disciplined convex programing
Lecture slides

Tentative Schedule :

Date Lecture Reading Contents

January 17 Lecture 1 Chapters1,2 Introduction, Convex Sets

January 22 Lecture 2 Chapters 1,2 Convex Sets

January 24 Lecture 3 Chapter 3 Convex Functions

January 29 Lecture 4 Chapter 3 Convex Functions

January 31 Lecture 5 Chapters 3,4 Convex Optimization Problems

February 5 Lecture 6 Chapter 4 Convex Optimization Problems

February 7 Lecture 7 Chapter 4 Vector Optimization, Conic programming

February 12 Lecture 8 Chapter 5 Duality

February 14 Lecture 9 Chapter 5 Duality in Convex Optimization

February 19 Lecture 10 Chapter 5 Interpretations of duality

February 21 Lecture 11 Chapter 6 Approximation and fitting

February 28 Midterm Midterm Midterm

March 4 Lecture 12 Chapters 6,7 Approximation and fitting/ Statistics

March 6 Lecture 13 Chapter 7,8 Geometric Problems, Distance Geometry

March 7-17 Spring Break Spring Break Spring Break

March 18 Lecture 14 Notes Numerical Linear Algebra

March 20 Lecture 15 Chapter 9 Unconstrained Minimization

March 25 Lecture 16 Chapter 9 Unconstrained Minimization

March 27 Lecture 17 Chapter 10 Equality Constrained Minimization

April 1 Lecture 18 Chapter 10 Equality Constrained Minimization

April 3 Lecture 19 Chapter 11 Interior point methods

April 8 Lecture 20 Chapter 11 Interior point Methods

April 10 LECTURE 21 Chapter 11 Complexity of Interior point methods

April 15 Lecture 22 Chapter 9,11 Self Concordant Functions

April 17 Lecture 23 Notes Advanced topics: SOS optimization

April 22 LECTURE 24 Notes Sum of Squares Methods

April 24 Lecture 25 Notes Advanced Topics

April 29 Lecture 26 Notes Review/Take Home Final

Date	Lecture	Reading	Contents
January 17	Lecture 1	Chapters1,2	Introduction, Convex Sets
January 22	Lecture 2	Chapters 1,2	Convex Sets
January 24	Lecture 3	Chapter 3	Convex Functions
January 29	Lecture 4	Chapter 3	Convex Functions
January 31	Lecture 5	Chapters 3,4	Convex Optimization Problems
February 5	Lecture 6	Chapter 4	Convex Optimization Problems
February 7	Lecture 7	Chapter 4	Vector Optimization, Conic programming
February 12	Lecture 8	Chapter 5	Duality
February 14	Lecture 9	Chapter 5	Duality in Convex Optimization
February 19	Lecture 10	Chapter 5	Interpretations of duality
February 21	Lecture 11	Chapter 6	Approximation and fitting
February 28	Midterm	Midterm	Midterm
March 4	Lecture 12	Chapters 6,7	Approximation and fitting/ Statistics
March 6	Lecture 13	Chapter 7,8	Geometric Problems, Distance Geometry
March 7-17	Spring Break	Spring Break	Spring Break
March 18	Lecture 14	Notes	Numerical Linear Algebra
March 20	Lecture 15	Chapter 9	Unconstrained Minimization
March 25	Lecture 16	Chapter 9	Unconstrained Minimization
March 27	Lecture 17	Chapter 10	Equality Constrained Minimization
April 1	Lecture 18	Chapter 10	Equality Constrained Minimization
April 3	Lecture 19	Chapter 11	Interior point methods
April 8	Lecture 20	Chapter 11	Interior point Methods
April 10	LECTURE 21	Chapter 11	Complexity of Interior point methods
April 15	Lecture 22	Chapter 9,11	Self Concordant Functions
April 17	Lecture 23	Notes	Advanced topics: SOS optimization
April 22	LECTURE 24	Notes	Sum of Squares Methods
April 24	Lecture 25	Notes	Advanced Topics
April 29	Lecture 26	Notes	Review/Take Home Final

Last modified : January 14, 2008. Send comments to Ali Jadbabaie

ESE 605: Modern Convex Optimization