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 - TY - CHAP A1 - Sharma, Kartikey A1 - Hendrych, Deborah A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Network Design for the Traffic Assignment Problem with Mixed-Integer Frank-Wolfe T2 - Proceedings of INFORMS Optimization Society Conference Y1 - 2024 ER - TY - CHAP A1 - Mexi, Gioni A1 - Shamsi, Somayeh A1 - Besançon, Mathieu A1 - Bodic, Pierre T1 - Probabilistic Lookahead Strong Branching via a Stochastic Abstract Branching Model T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2024 N2 - Strong Branching (SB) is a cornerstone of all modern branching rules used in the Branch-and-Bound (BnB) algorithm, which is at the center of Mixed-Integer Programming solvers. In its full form, SB evaluates all variables to branch on and then selects the one producing the best relaxation, leading to small trees, but high runtimes. State-of-the-art branching rules therefore use SB with working limits to achieve both small enough trees and short run times. So far, these working limits have been established empirically. In this paper, we introduce a theoretical approach to guide how much SB to use at each node within the BnB. We first define an abstract stochastic tree model of the BnB algorithm where the geometric mean dual gains of all variables follow a given probability distribution. This model allows us to relate expected dual gains to tree sizes and explicitly compare the cost of sampling an additional SB candidate with the reward in expected tree size reduction. We then leverage the insight from the abstract model to design a new stopping criterion for SB, which fits a distribution to the dual gains and, at each node, dynamically continues or interrupts SB. This algorithm, which we refer to as Probabilistic Lookahead Strong Branching, improves both the tree size and runtime over MIPLIB instances, providing evidence that the method not only changes the amount of SB, but allocates it better. Y1 - 2024 U6 - https://doi.org/10.1007/978-3-031-60599-4_4 VL - 14743 ER - TY - JOUR A1 - Designolle, Sébastien A1 - Iommazzo, Gabriele A1 - Besançon, Mathieu 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 - Besançon, Mathieu A1 - Garcia, Joaquim Dias A1 - Legat, Benoît A1 - Sharma, Akshay T1 - Flexible Differentiable Optimization via Model Transformations JF - INFORMS Journal on Computing N2 - We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus leveraging the rich ecosystem of solvers and composing well with modeling languages like JuMP. DiffOpt offers both forward and reverse differentiation modes, enabling multiple use cases from hyperparameter optimization to backpropagation and sensitivity analysis, bridging constrained optimization with end-to-end differentiable programming. DiffOpt is built on two known rules for differentiating quadratic programming and conic programming standard forms. However, thanks to its ability to differentiate through model transformations, the user is not limited to these forms and can differentiate with respect to the parameters of any model that can be reformulated into these standard forms. This notably includes programs mixing affine conic constraints and convex quadratic constraints or objective function. Y1 - 2023 U6 - https://doi.org/10.1287/ijoc.2022.0283 VL - 36 IS - 2 SP - 456 EP - 478 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Besançon, Mathieu A1 - Chen, Wei-Kun A1 - Chmiela, Antonia A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Gaul, Oliver A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc E. A1 - Rehfeldt, Daniel A1 - Schlein, Steffan A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Sofranac, Boro A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Wellner, Philipp A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 8.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack. T3 - ZIB-Report - 21-41 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85309 SN - 1438-0064 ER - TY - GEN A1 - Bolusani, Suresh A1 - Besançon, Mathieu A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Dionísio, João A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Ghannam, Mohammed A1 - Gleixner, Ambros A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hedtke, Ivo A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Kamp, Dominik A1 - Koch, Thorsten A1 - Kofler, Kevin A1 - Lentz, Jurgen A1 - Manns, Julian A1 - Mexi, Gioni A1 - Mühmer, Erik A1 - E. Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Xu, Liding T1 - The SCIP Optimization Suite 9.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver. T3 - ZIB-Report - 24-02-29 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-95528 SN - 1438-0064 ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Besançon, Mathieu A1 - Chen, Wei-Kun A1 - Chmiela, Antonia A1 - Donkiewicz, Tim A1 - Doornmalen, Jasper A1 - Eifler, Leon A1 - Gaul, Oliver A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - Hulst, Rolf A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Rehfeldt, Daniel A1 - Schlein, Steffan A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Sofranac, Boro A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Wellner, Philipp A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - Enabling research through the SCIP optimization suite 8.0 JF - ACM Transactions on Mathematical Software N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP. Y1 - 2023 U6 - https://doi.org/10.1145/3585516 VL - 49 IS - 2 SP - 1 EP - 21 ER - TY - CHAP A1 - Mexi, Gioni A1 - Besançon, Mathieu A1 - Bolusani, Suresh A1 - Chmiela, Antonia A1 - Hoen, Alexander A1 - Gleixner, Ambros T1 - Scylla: a matrix-free fix-propagate-and-project heuristic for mixed-integer optimization T2 - Proceedings of Conference of the Society for Operations Research in Germany Y1 - 2023 ER - TY - JOUR A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a $4\%$ decrease in solve time, and an $8\%$ decrease in number of nodes over affected instances of MIPLIB 2017. Y1 - 2023 PB - Springer ER -