Jonathan Eckstein's Special Topics in Management Science: Convex Analysis and Optimization Graduate Class 26:711:685:03

 
For my similar course given in the New Brunswick graduate school in Fall 2011, see here.
 

Announcements (As of December 20, 2013 10:27 PM)

• The second take-home has been graded.  Exam scores and overall course grades may be viewed on "Gradebook 2" in Sakai, and I have submitted course grades to the registrar.  The solution may be viewed on Sakai.  I hope everybody had an illuminating semester, and best wishes for the holidays.
    

Usual Office Hour Schedule

My office is 100 Rockafeller Road building, room 5145.   My planned office hours for Fall 2013 are:

• Tuesdays 1:30-3:30 PM, September 10 - December 10
• Wednesdays 12:30-2:30 PM, September 11 - December 4
• Or other times by appointment
• Note that exceptions will be posted above
   

Handouts, Class Materials, and Assignments

1. Thursday, September 5:  Introduction, basic convexity concepts -- convex sets, epigraphs, convex functions, closed/lower semicontinuous functions, differentiable convex functions, convex and affine hulls
   • Syllabus (PDF format)
2. Thursday, September 12:  A bit more on differentiable convex functions, combinations and hulls, cones, Caratheodory's theorem, relative interiors
   • Homework 1, due September 19
3. Thursday, September 19:  Finish relative interiors, basics of optimization, start projection
   • Homework 2, due September 26 (disregard problem 3, which will be moved to a later homework)
   • Please read Section 1.5 of the text, regarding recession cones.  Most of the proofs are not critical, except Proposition 1.5.1 (a)-(c) and especially (b).  I did not have time to cover this material in class.
4. Thursday, September 26:  Finish projection, separation
5. Thursday, October 3:  Polar and dual cones, polyhedral cones and sets
   • Homework 3, due October 10
6. Thursday, October 10: Subgradients and subdifferential calculus
   • Homework 4, due October 17
7. Thursday, October 17:  Proof of (simplified) Rockafeller-Moreau theorem, deriving optimality conditions and constraint qualifications from the Rockafeller-Moreau theorem (also, start conjugate functions if time permits)
   • Homework 5 (take-home midterm), due October 24 (with corrected due date and minor typo correction as of November 18; assumption added to problem 1 on November 22) -- due date postponed to October 31.
8. Thursday, October 24:  Conjugate functions
9. Thursday, October 31:  Fenchel and parametric duality for optimization problems
   • Homework 6, due November 7 (with typos corrected November 5)
10. Thursday, November 7:  More parametric duality
11. Thursday, November 14:  More parametric duality, monotone operators
    • Homework 7, due November 14
12. Thursday, November 21:  Monotone operators, nonexpansiveness, finding fixed points of nonexpansive maps
13. Tuesday, November 26:  The proximal point algorithm, augmented Lagrangian algorithms
    • Homework 8 (take-home) final, due December 17 (3:30pm) (on Sakai)
14. Thursday, December 5:  More augmented Lagrangian algorithms, the alternating direction method of multipliers (ADMM)
     

Homework solutions

Solutions are posted on Sakai.

• Solution to homework 1
• Solution to homework 2
• Solution to homework 3
• Solution to homework 4
• Solution to homework 5 (first take-home)
• Solution to homework 6
• Solution to homework 7
• Solution to homework 8 (second take-home)