Jonathan Eckstein's Convex Analysis and Optimization Doctoral Class 16:711:558

For my similar special topics course given Spring 2009, see here.

Announcements (As of August 20, 2013 02:01 PM)

Usual Office Hour Schedule

Regular office hours this semester are at RUTCOR:

Check the announcements section above for occasional office hour changes and cancellations.

Handouts, Class Materials, and Assignments

  1. September 7:  Introduction, basic convexity concepts -- convex sets, epigraphs, convex functions, closed/lower semicontinuous functions, differentiable convex functions, convex and affine hulls
  2. September 14:  More basic convexity concepts -- cones, Carathéodory's theorem, relative interiors
  3. September 21:  Recession cones, generalized Weierstrass results, local versus global minima, projection
  4. September 28:  Separation and polarity
  5. October 5:  Polyhedral sets and cones, subgradients
  6. October 12:  Monotonicity of subgradients, normal cones, sampling of subdifferential calculus, start constrained optimality
  7. October 19:  Conic approximations, Lagrange multiplier conditions for equality constraints
  8. October 26:  Lagrange multiplier conditions for inequality constraints, start conjugate functions
  9. November 2: Duality of conjugate functions, simple Fenchel-style duality for optimization problems
  10. November 9: Examples of Fenchel duality, biconjugate (Rockafellar) duality
  11. November 16:  More biconjugate duality, start subgradient algorithms
  12. November 21 (Monday):  Convergence analysis of subgradient algorithms, proximal minimization algorithms
  13. November 30:  Augmented Lagrangian algorithms
  14. December 6 (Tuesday night):  finish augmented Lagrangian algorithms, overview of bundle methods

Homework solutions

Solutions are posted on Sakai.