Mathieu Besançon, Ralf Borndörfer, Sebastian Pokutta
01.04.2023 – 31.03.2026
We want to investigate mixed-integer optimization with a convex differentiable objective and solution approaches based on error-adaptive convex solvers in branch-and-bound. We will focus on lower bound improvements within the tree and the tradeoff between the lower bound increase and computational costs of strong relaxations.
We aim to develop a branch-and-bound-based methodology for mixed-integer convex problems that accelerates the solution process by taking advantage of the specificities of modern MILP techniques and error-adaptive first-order methods.
Two aspects that will in particular be developed and exploited are warm-starting in convex and mixed-integer linear optimization, and early termination resulting in the controlled inexactness of some oracles.
Hendrych, Deborah, Hannah Troppens, Mathieu Besançon, and Sebastian Pokutta. “Convex integer optimization with Frank-Wolfe methods.” arXiv preprint arXiv:2208.11010 (2022).
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