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)
- Due to a prior travel commitment December 7-19, the last class will be
held 6:40-9:30pm on Tuesday, December 6, instead of December 7. We
will meet in the RUTCOR lounge, room 166.
- The second take-home / homework 7 will be distributed in class on
December 6. It will be due by 10am Tuesday,
December 20. If you wish to hand it in before December 20, please give
it to Clare Smietana in RUTCOR 123-A.
Usual Office Hour Schedule
Regular office hours this semester are at RUTCOR:
- Tuesdays 2:00-3:30 PM, starting September 13, ending December 6
- Or other times by appointment
Check the announcements section above for
occasional office hour
changes and cancellations.
Handouts, Class Materials, and Assignments
- September 7: Introduction, basic convexity concepts -- convex sets,
epigraphs, convex functions, closed/lower semicontinuous functions,
differentiable convex functions, convex and affine hulls
- September 14: More basic convexity concepts -- cones,
Carathéodory's theorem, relative interiors
- September 21: Recession cones, generalized Weierstrass
results, local versus global minima, projection
- September 28: Separation and polarity
- October 5: Polyhedral sets and cones, subgradients
- October 12: Monotonicity of subgradients, normal cones, sampling of
subdifferential calculus, start constrained optimality
- October 19: Conic approximations, Lagrange multiplier conditions for
equality constraints
- October 26: Lagrange multiplier conditions for inequality
constraints, start conjugate functions
- November 2: Duality of conjugate functions, simple Fenchel-style duality
for optimization problems
- November 9: Examples of Fenchel duality, biconjugate (Rockafellar) duality
- November 16: More biconjugate duality, start subgradient algorithms
- November 21 (Monday): Convergence analysis of subgradient
algorithms, proximal minimization algorithms
- November 30: Augmented Lagrangian algorithms
- December 6 (Tuesday night): finish augmented Lagrangian algorithms,
overview of bundle methods
Homework solutions
Solutions are posted on Sakai.