Solution Techniques for Mixed-integer Nonconvex Optimization ongoing

We want to investigate (mixed-)integer optimization with a non-convex, differentiable objective within a Branch-and-Bound framework utilizing Frank-Wolfe methods as node solvers. The focus lies on incorporating spatial branching in the current framework and to compare it to convexification strategies.

MATH+ AA-Mobil-1
Sep 2025 to Aug 2028
3

🧑‍🎓 Project Members

Mathieu Besançon
Principal Investigator
besancon (at) zib.de
Sebastian Pokutta
Principal Investigator
pokutta (at) zib.de
Deborah Hendrych
hendrych (at) zib.de

🪙 Funding

This project is being funded by the Berlin Mathematics Research Center MATH+ (project ID AA-Mobil-1), itself funded by the German Research Foundation (DFG) under Germany's Excellence Strategy (EXC-2046/1, project ID 390685689) from September 2025 to August 2028.

🔬 Project Description

The project will investigate two main approaches: (1) Automatic Convexification - developing systematic methods to add polynomial terms to objective functions that preserve optimal solutions while making problems more tractable, extending techniques from binary to general integer cases; and (2) Spatial Branching - integrating advanced branching strategies with partial convexification to handle broader problem classes, including parallelization of bound computations and leveraging existing techniques like warm-starting and early termination to improve computational efficiency. The overall goal is to create a comprehensive framework that balances convexification benefits with computational performance through strategic partial convexification and enhanced branching methods.