Solving Mixed-Integer Semidefinite Programs
Vortragender: Prof. Dr. Marc Pfetsch
Semidefinite programs try to optimize a positive semidefinite matrix subject to linear inequality constraints. This class can be extended to mixed-integer semidefinite programs in which some of the variables are required to be integer. This forms an interesting class of optimization problems with many applications. This talk will introduce new methods as well as techniques that can be generalized from the linear to the semidefinite world. This includes presolving methods, e.g., fixing of variables, bound strengthening etc. Moreover, handling of symmetries and so-called conflict analysis can be adapted and have a positive impact on the performance. The impact of the methods will be illustrated computationally, using SCIP-SDP, an open-source solver for mixed-integer semidefinite programs based on SCIP.