The day began with a plenary talk by Stephen Boyd on “Real-Time Embedded Convex Optimization”. He started by saying there would be no new theory. His talk was about solving convex optimization problems in milliseconds or microseconds. Why bother? Because in real-time applications you may need to solve the same (little) problem over and over. He showed a number of examples with applications including signal processing, control, and my favorite, grasp force optimization: you are given an object to which a force and a rotation are applied, together with potential grasp points. Your task is to decide where a robotic arm should hold the object (and with which intensity) so that it counter acts the given forces. It turns out that if you have 5 potential grasp points, you can roughly solve 20 thousand of these problems in one second! Robots do not need to grasp 20K things in one second, but this could be used to choose the best set of grasp points quickly.
During the regular sessions, I attended a number of talks on generating cutting planes from multiple (rather than one) rows of the Simplex tableau. This seems to be a pretty hot area of research since the recent paper by Kent Andersen (one of my former office mates at Tepper!), Quentin Louveaux, Robert Weismantel and Laurence Wolsey, which appeared in IPCO 2007. I enjoyed those talks very much, including the ones by François Margot, Egon Balas, Robert Weismantel and Andrea Lodi, but I must confess that I need to do some (a lot of) reading to really be able to grasp all the details. Nevertheless, I learned (among other things) that finding all the possible kinds of maximal lattice-free sets in 3 dimensions is not a trivial task (in 2-D, they can only be strips, triangles or quadrilaterals). The morning session on recent improvements on MIP solvers (which included Gurobi and CPLEX) was overflowing with people. There was no space to even sit on the floor, and a number of people (including me) stood outside the room. I also attended John Hooker‘s talk on SIMPL, and I was happy to see the room almost full.
During the breaks between sessions, I ran into a number of (other) old friends and we had very nice chats. I also met a few new people (many doing their PhD at Tepper), so the networking part has been going pretty well so far. I found out that you can pre-order the book on “A Brief History of the International Symposia on Mathematical Programming”, by Richard Cottle of Stanford University (see photo below), for $20. It apparently takes about a month to arrive.
The day ended with two parallel semi-plenaries given by Mihai Anitescu (“The Challenge of Large-Scale Differential Variational Inequalities”) and Éva Tardos (“Games in Networks: The Price of Anarchy, Stability, and Learning”). I chose to go to Éva’s talk. The central question was whether natural behavior leads to Nash equilibrium in learning games. She proceeded to define what a “natural” learning method could look like and showed that it converges to a weakly stable equilibrium that’s pretty close (in a probabilistic way) to pure Nash equilibrium.
Finally, I know that this is not a Food Network website, but I must share the following two pieces of information: (1) DO NOT order the Pad Thai at DAO restaurant at 230 E Ohio St, and (2) DO go to the India House restaurant at 59 W Grand Avenue (their Vegetarian Thali was delicious).
That’s it for today. I have a date with Latex Beamer (no, that’s not a newly released BMW convertible) for the next couple of hours.
Here’s a couple of photos:
Ballroom where plenaries are held
Book on history of ISMP