Algebraic and Geometric Ideas in Linear Optimization
Jesus De Loera
Department of Mathematics
University of California Davis
Linear programming is undeniably a central software tool of applied mathematics and a source of many fascinating mathematical problems. In this talk I will present several advances from the past 5 years in the theory of algorithms in linear optimization. These results include new results on the complexity of the simplex method, the structure of central paths of interior point methods, and about the geometry of some less well-known iterative techniques. One interesting feature of these advances is that they connect this very applied algorithmic field with topics that are often not thought as applied such as algebraic geometry and combinatorial topology.