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)

Usual Office Hour Schedule

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

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
  2. Thursday, September 12:  A bit more on differentiable convex functions, combinations and hulls, cones, Caratheodory's theorem, relative interiors
  3. Thursday, September 19:  Finish relative interiors, basics of optimization, start projection
  4. Thursday, September 26:  Finish projection, separation
  5. Thursday, October 3:  Polar and dual cones, polyhedral cones and sets
  6. Thursday, October 10: Subgradients and subdifferential calculus
  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)
  8. Thursday, October 24:  Conjugate functions
  9. Thursday, October 31:  Fenchel and parametric duality for optimization problems
  10. Thursday, November 7:  More parametric duality
  11. Thursday, November 14:  More parametric duality, monotone operators
  12. Thursday, November 21:  Monotone operators, nonexpansiveness, finding fixed points of nonexpansive maps
  13. Tuesday, November 26:  The proximal point algorithm, augmented Lagrangian algorithms
  14. Thursday, December 5:  More augmented Lagrangian algorithms, the alternating direction method of multipliers (ADMM)

Homework solutions

Solutions are posted on Sakai.