Citation: The poster committee found Leon Eifler's computational work on exact rational integer programming outstanding. It takes a significant step into closing the gap between exact arithmetic MIP solvers and their finite-precision counterparts, and the work substantially builds upon its predecessor. In this 2.0 version, we see an integration of many important tools such as presolve, optimality certification, and heuristics.

Citation: Kevin's poster studies an innovative approach to approximate SDPs by replacing the full PSD requirement with only locally PSD requirements originating from the underlying graph structure of the problem data. The poster introduces a key parameter to measure the approximation quality and presents a multiplicative approximation guarantee on the quality of the resulting locally sparse approximation for Max-Cut type SDPs. In addition, for specific graphs including chordal graphs and series parallel graphs, precise values of this key approximation approximation parameter were given along with a number of graph operations preserving the value of the parameter.

Citation: Aleksandr's poster contributes to our fundamental understanding of semidefinite programs (SDPs). It shows that any strictly feasible SDP can be converted into a special form with exponentially-large solutions (in terms of the size of the input) via a change of basis, thereby demonstrating that numerically challenging models are not too rare in theory. Moreover, though the solutions for SDPs in this special form are of exponential size, the poster shows how to certify their existence in polynomial space. The poster makes significant progress in addressing the open question "Can we decide feasibility of SDPs in polynomial time?", among other applications.