TY - JOUR A1 - Designolle, Sébastien A1 - Besançon, Mathieu A1 - Iommazzo, Gabriele A1 - Knebel, Sebastian A1 - Gelß, Patrick A1 - Pokutta, Sebastian T1 - Improved Local Models and New Bell Inequalities Via Frank-Wolfe Algorithms JF - Physical Review Research N2 - In Bell scenarios with two outcomes per party, we algorithmically consider the two sides of the membership problem for the local polytope: Constructing local models and deriving separating hyperplanes, that is, Bell inequalities. We take advantage of the recent developments in so-called Frank-Wolfe algorithms to significantly increase the convergence rate of existing methods. First, we study the threshold value for the nonlocality of two-qubit Werner states under projective measurements. Here, we improve on both the upper and lower bounds present in the literature. Importantly, our bounds are entirely analytical; moreover, they yield refined bounds on the value of the Grothendieck constant of order three: 1.4367⩽KG(3)⩽1.4546. Second, we demonstrate the efficiency of our approach in multipartite Bell scenarios, and present local models for all projective measurements with visibilities noticeably higher than the entanglement threshold. We make our entire code accessible as a julia library called BellPolytopes.jl. Y1 - 2023 U6 - https://doi.org/10.1103/PhysRevResearch.5.043059 VL - 5 SP - 043059 ER - TY - JOUR A1 - Hendrych, Deborah A1 - Troppens, Hannah A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Convex mixed-integer optimization with Frank-Wolfe methods JF - Mathematical Programming Computation Y1 - 2025 U6 - https://doi.org/10.1007/s12532-025-00288-w VL - 17 SP - 731 EP - 757 ER - TY - CHAP A1 - Hendrych, Deborah A1 - Besançon, Mathieu A1 - Martínez-Rubio, David A1 - Pokutta, Sebastian T1 - Secant line search for Frank-Wolfe algorithms T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/hendrych25a/hendrych25a.pdf VL - 267 SP - 23005 EP - 23029 ER - TY - JOUR A1 - Bolusani, Suresh A1 - Besançon, Mathieu A1 - Gleixner, Ambros A1 - Berthold, Timo A1 - D'Ambrosio, Claudia A1 - Muñoz, Gonzalo A1 - Paat, Joseph A1 - Thomopulos, Dimitri T1 - The MIP workshop 2023 computational competition on reoptimization JF - Mathematical Programming Computation N2 - This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge was to accelerate the proof of optimality of the modified instances by leveraging the information from the solving processes of previously solved instances, all while creating high-quality primal solutions. Specifically, we discuss the competition’s format, the creation of public and hidden datasets, and the evaluation criteria. Our goal is to establish a methodology for the generation of benchmark instances and an evaluation framework, along with benchmark datasets, to foster future research on reoptimization of mixed integer linear optimization problems. Y1 - 2024 U6 - https://doi.org/10.1007/s12532-024-00256-w VL - 16 SP - 255 EP - 266 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Scalable Frank-Wolfe on generalized self-concordant functions via simple steps JF - SIAM Journal on Optimization Y1 - 2024 U6 - https://doi.org/10.1137/23M1616789 VL - 34 IS - 3 ER - TY - CHAP A1 - Hendrych, Deborah A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Solving the optimal experiment design problem with mixed-integer convex methods T2 - 22nd International Symposium on Experimental Algorithms (SEA 2024) N2 - We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained about the system from the observations, leading to a convex integer optimization problem. We leverage Boscia.jl, a recent algorithmic framework, which is based on a nonlinear branch-and-bound algorithm with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which is preserved by the method, unlike alternative methods relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of our proposed method, especially on large and challenging instances. Y1 - 2024 U6 - https://doi.org/10.4230/LIPIcs.SEA.2024.16 VL - 301 SP - 16:1 EP - 16:22 ER - TY - JOUR A1 - Wilken, St. Elmo A1 - Besançon, Mathieu A1 - Kratochvíl, Miroslav A1 - Kuate, Chilperic Armel Foko A1 - Trefois, Christophe A1 - Gu, Wei A1 - Ebenhöh, Oliver T1 - Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models JF - Metabolic Engineering Y1 - 2022 ER - TY - CHAP A1 - Troppens, Hannah A1 - Besançon, Mathieu A1 - Wilken, St. Elmo A1 - Pokutta, Sebastian T1 - Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks T2 - 23rd International Symposium on Experimental Algorithms (SEA 2025) Y1 - 2025 U6 - https://doi.org/10.4230/LIPIcs.SEA.2025.26 VL - 338 SP - 26:1 EP - 26:18 PB - Schloss Dagstuhl – Leibniz-Zentrum für Informatik ER - TY - CHAP A1 - Besançon, Mathieu A1 - Pokutta, Sebastian A1 - Wirth, Elias T1 - The Pivoting Framework: Frank-Wolfe Algorithms with Active Set Size Control T2 - Proceedings of The 28th International Conference on Artificial Intelligence and Statistics Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v258/main/assets/besancon25a/besancon25a.pdf VL - 258 SP - 271 EP - 279 ER - TY - CHAP A1 - MacDonald, Jan A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderings T2 - Proceedings of the International Conference on Machine Learning Y1 - 2022 ER -