### ESE 605: Modern Convex Optimization

Department of Electrical and Systems Engineering
University of Pennsylvania

Spring 2009

• Announcements :
• First class is on January 15 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:
• Lectures: Tuesdays and Thursdays 3:00pm-4:30pm in Towne 309

• Required Text
• Other References

• Grading:
• Homework : 30%
• Midterm : 30%
• Final : 40%

• Teaching assistants:

• Further review and reading

• Assignments and homework sets:

• Homework 1: Reading: Chapter 2 of Boyd and Vandenberghe. Problems 2.1, 2.3, 2.7, 2.8(a,c,d), 2.10, 2.18, 2.19. Due on Thursday January 29th.

• Homework 2: Reading: Chapter 3 of Boyd and vandenberghe. Problems 2.20,2.33, 2.34, 2.36, 3.2, 3.7, 3.16, 3.20. Due on Thursday February 5th.

• Homework 3: Problems 3.18, 3.23(b), 3.24(a,d,e), 3.25, 3.26(a,b), 3.37. Due on Thursday February 12th.

• Homework 4: Problems 3.43, 3.47, 3.57, 4.2, 4.6, 4.9. Due on Thursday February 19th.

• Homework 5: Problems , 4.13,4.21 (c), 4.26, 4.34, 4.40(c), 4.41, 4.44 . Due on Thursday March 5.

• Homework 6: Problems 4.45, 5.9, 5.11, 5.12, 5.14, 5.35. Due on Tuesday March 19.
• Homework 8: Problems 9.7, 9.8, 9.17 (c), 9.18, 9,27, 9.30. Due on Tuesday April 14
• Homework 9: Problems 10.14, 10.15, 11.5, 11.6, 11.7, 11.9. Due with the Take-home exam.

• Other resources:

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

• Lecture slides
• Tentative Schedule :

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

Last modified : January 13, 2009. Send comments to Ali Jadbabaie