Recent Topics in Mixed Integer Programming

This talk presents computational and theoretical advances/experiments in Mixed Integer Nonlinear Programming across two complementary themes. The first focuses on emerging MINLP techniques — online learning for pseudo cost estimation, ReLU-based neural methods for cut separation, and AlphaEvolve-style modelling — that aim to modernize the MINLP solver. The second focuses on aggregation-based cutting planes, highlighting the practical importance of Complemented Mixed Integer Rounding (CMIR) cuts in modern MILP solvers. A sparsity-driven aggregation framework is introduced that models aggregation as an MILP and a two-stage LP heuristic that produces sparse, strong aggregated rows with measurable gains on MIPLIB2017. Theoretical results show CMIR cuts frequently define faces (and empirically facets) of the convex hull; Fenchel-style normalization is proposed to strengthen them. Finally, we give a prospect on the MINLP solving.