Abstract: The presence of floating-point roundoff errors compromises the results of virtually all fast mixed-integer programming solvers available today.

In this talk, we present recent advances in our endeavour to craft a performant mixed-integer optimizer that is not only free from roundoff errors but produces certificates of optimality that can be verified independently of the solving process. Key to most efficient techniques is the combination of different levels of arithmetic precision and the use of directed rounding. We highlight several methods that follow this paradigm and present advances in exact LP solving and the safe generation of Gomory mixed-integer cuts via mixed-integer rounding. Our computational experiments are based on an extension of the open-source solver SCIP and the certificate language VIPR. This is joint work with Sander Borst. Leon Eifler, Fabian Frickenstein, and Jules Nicolas-Thouvenin.

Bio: Ambros Gleixner is Professor for Discrete Mathematics and Operations Research at HTW Berlin and Head of the research group Mathematical Optimization Methods at Zuse Institute Berlin (ZIB). He received both his diploma and Ph.D. degree in mathematics from the TU Berlin in Germany.