Title: How we solve linear programs
| Speaker: | Laurent Poirrier |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract:
Linear programming is one of the most fundamental tools in optimization, and its theoretical complexity is well understood. In practice though, things are quite different: Which types of problems can we really solve? What sizes? With what algorithms? We will cover the state of the art, which has been dominated by closed-source commercial solvers. Then, we will present a new implementation of the simplex method, which is competitive with the best commercial solvers.
We will show how having access to the implementation details of an LP code allows us to develop and test interesting ideas. In particular, we will describe a new factorization update method that can be performed just by looking at the nonzero structure of the matrices, without any algebra. This method speeds up our code by a few percents, and is now enabled by default in our solver. No prior computational knowledge will be assumed in this talk.