FWF Project P12660-MAT „Semidefinite programs and discrete optimization“

The project aims at applying semidefinite programming, a natural generalization of linear programming, to integer programming problems. The project has three main goals. First, the question of modeling general integer programs in the framework of semidefinite programming is investigated. These investigations focus on the interplay between semidefinite programs and linear cutting planes. Secondly, purely algorithmic aspects to efficiently solve semidefinite programs are considered. There are a variety of strategies to derive search directions, but it is currently not clear which of these approaches are most efficient. Finally, the question of solving (or at least approximating) large scale (but sparse) problems is considered by applying eigenvalue optimization and nonsmooth optimization techniques. Since 1999 the project is carried out at the University of Klagenfurt.