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

- 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.

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

- 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)

- Thursday, September 12: A bit more on differentiable convex functions, combinations and hulls, cones, Caratheodory's theorem, relative interiors
- 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.

- Thursday, September 26: Finish projection, separation
- Thursday, October 3: Polar and dual cones, polyhedral cones and sets
- Thursday, October 10: Subgradients and subdifferential calculus
- 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.

- Thursday, October 24: Conjugate functions
- Thursday,
October 31: Fenchel and parametric duality for optimization problems
- Homework 6, due November 7 (with typos corrected November 5)

- Thursday, November 7: More parametric duality
- Thursday, November 14: More parametric duality, monotone operators
- Thursday, November 21: Monotone operators, nonexpansiveness, finding fixed points of nonexpansive maps
- Tuesday, November 26: The proximal point algorithm, augmented
Lagrangian algorithms
- Homework 8 (take-home) final, due December 17 (3:30pm) (on Sakai)

- Thursday, December 5: More augmented Lagrangian algorithms, the
alternating direction method of multipliers (ADMM)

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)