Jonathan Eckstein's Convex Analysis and Optimization Doctoral Class 16:711:611
Official Title: Special Topics in Operations Research

Announcements (As of July 29, 2011 11:35 AM)

• I have graded homework 7 and returned it to students' RUTCOR mailboxes (except for Dan; I have his homework in my office).
• I have submitted the course grades to the RUTCOR office (the online system would not accept them for some reason)
   
• Regular office hours are over for the semester as of April 30.

Usual Office Hour Schedule

I plan on holding office hours at RUTCOR this semester:

• Tuesdays 2:00-3:30 PM
• Or other times by appointment

This schedule may be changed if it conflicts with student schedules.  Check the announcements section above for occasional office hour changes and cancellations.
 

Handouts, Class Materials, and Assignments

1. January 21:  Introduction, basic convexity concepts
   • Syllabus (PDF format)
   • Homework 1, due January 28
2. January 28:  More basic convexity
   •  Originally intended version of homework 2, now superseded
3. February 4:  Finish basic convexity (recession cones), fundamental optimization results, projection, separation
   • Homework 2, due February 11 (with corrections as of February 8; extension: due date changed to February 18).
4. February 11:  Separation theorems, Bertsekas simplified duality
5. February 18:  Strong duality theorem for simplified duality framework, polar cones, polyhedral cones and sets
   • Homework 3, due February 25 (minor correction made February 23)
6. February 25:  Extreme points, directional derivatives, subgradients
7. March 4:  Elements of subdifferential calculus, feasible direction and tangent cones
   • Homework 4, due March 25
8. March 11:  Normal cones, conic and variational optimality conditions, introduction to Lagrange multipliers
9. March 25:  Lagrange multipliers
10. April 1:  Slater's condition, conjugate functions
    • Homework 5, due April 8
11. April 8:  Finish conjugate functions, Fenchel-like duality, start Rockafellar conjugate duality
12. April 15:  Strong duality and other topics in the Rockafellar framework
    • Homework 6, due April 24 (postponed by request from April 22)
13. April 22:  Subgradient and Lagrangian relaxation algorithms
    • Homework 7, due April 29 (typos corrected for second time April 28, due date extended by request to May1)
14. April 29:  Proximal minimization and augmented Lagrangian methods

Homework solutions

1. Solution to homework 1
2. Solution to homework 2
3. Solution to homework 3 (minor updates made March 4)
4. Solution to homework 4
5. Solution to homework 5
6. Solution to homework 6
7. Solution to homework 7