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title={Relativity: the Special and General Theory},
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author={Einstein, Albert},
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year={1920},
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publisher={Methuen & Co Ltd},
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html={relativity.html}
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@article{hendrych2023convex,
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title={Convex mixed-integer optimization with {Frank-Wolfe} methods},
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author={Deborah Hendrych and Hannah Troppens and Mathieu Besançon and Sebastian Pokutta},
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journal={Mathematical Programming Computation},
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year={2025},
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abstract={Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex node relaxations. These relaxations are solved with a Frank–Wolfe algorithm over the convex hull of mixed-integer feasible points instead of the continuous relaxation via calls to a mixed-integer linear solver as the linear minimization oracle. The proposed method computes feasible solutions while working on a single representation of the polyhedral constraints, leveraging the full extent of mixed-integer linear solvers without an outer approximation scheme and can exploit inexact solutions of node subproblems.},
title={Improved algorithms and novel applications of the {FrankWolfe.jl} library},
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author={Besan{\c{c}}on, Mathieu and Designolle, S{\'e}bastien and Halbey, Jannis and Hendrych, Deborah and Kuzinowicz, Dominik and Pokutta, Sebastian and Troppens, Hannah and Herrmannsdoerfer, Daniel Viladrich and Wirth, Elias},
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journal={ACM Transactions on Mathematical Software},
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year={2025},
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abstract={Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of the development of FrankWolfe.jl, a Julia package gathering high-performance implementations of state-of-the-art FW variants. We review key use cases of the library in the recent literature, which match its original dual purpose: first, becoming the de-facto toolbox for practitioners applying FW methods to their problem, and second, offering a modular ecosystem to algorithm designers who experiment with their own variants and implementations of algorithmic blocks. Finally, we demonstrate the performance of several FW variants on important problem classes in several experiments, which we curated in a separate repository for continuous benchmarking.},
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abbr={ACM TOMS},
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bibtex_show={true},
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title={Investigations on the Theory of the Brownian Movement},
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author={Einstein, Albert},
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year={1956},
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publisher={Courier Corporation},
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preview={brownian-motion.gif}
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selected={false},
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tags={Frank-Wolfe, Julia, convex optimization},
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pdf={https://dl.acm.org/doi/abs/10.1145/3765626}
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}
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@article{einstein1950meaning,
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abbr={AJP},
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@article{hendrych2025secant,
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title={Secant Line Search for {Frank-Wolfe} Algorithms},
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author={Hendrych, Deborah and Besan{\c{c}}on, Mathieu and Mart{\'\i}nez-Rubio, David and Pokutta, Sebastian},
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journal={PMLR},
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year={2025},
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abstract={We present a new step-size strategy based on the secant method for Frank-Wolfe algorithms. This strategy, which requires mild assumptions about the function under consideration, can be applied to any Frank-Wolfe algorithm. It is as effective as full line search and, in particular, allows for adapting to the local smoothness of the function, such as in (Pedregosa et al., 2020), but comes with a significantly reduced computational cost, leading to higher effective rates of convergence. We provide theoretical guarantees and demonstrate the effectiveness of the strategy through numerical experiments.},
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abbr={ICML25},
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bibtex_show={true},
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title={The meaning of relativity},
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author={Einstein, Albert and Taub, AH},
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journal={American Journal of Physics},
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volume={18},
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number={6},
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pages={403--404},
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year={1950},
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publisher={American Association of Physics Teachers}
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}
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@article{PhysRev.47.777,
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abbr={PhysRev},
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title={Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?},
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author={Einstein*†, A. and Podolsky*, B. and Rosen*, N.},
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abstract={In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.},
abstract={We propose a primal heuristic for quadratic mixed-integer problems. Our method extends the Boscia framework -- originally a mixed-integer convex solver leveraging a Frank-Wolfe-based branch-and-bound approach -- to address nonconvex quadratic objective and constraints. We reformulate nonlinear constraints, introduce preprocessing steps, and a suite of heuristics including rounding strategies, gradient-guided selection, and large neighborhood search techniques that exploit integer-feasible vertices generated during the Frank-Wolfe iterations. Computational results demonstrate the effectiveness of our method in solving challenging MIQCQPs, achieving improvements on QPLIB instances within minutes and winning first place in the Land-Doig MIP Computational Competition 2025.},
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author = {Mexi, Gioni and Hendrych, Deborah and Designolle, Sébastien and Besançon, Mathieu and Pokutta, Sebastian},
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title = {A {Frank-Wolfe}-based Primal Heuristic for Quadratic Mixed-integer Optimization},
booktitle = {Proceedings of the INFORMS Optimization Society Conference},
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archiveprefix = {arXiv},
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eprint = {2402.00166},
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abstract={We tackle the network design problem for centralized traffic assignment, which can be cast as a mixed-integer convex optimization (MICO) problem. For this task, we propose different formulations and solution methods in both a deterministic and a stochastic setting in which the demand is unknown in the design phase. We leverage the recently proposed Boscia framework, which can solve MICO problems when the main nonlinearity stems from a differentiable objective function. Boscia tackles these problems by branch-and-bound with continuous relaxations solved approximately with Frank-Wolfe algorithms. We compare different linear relaxations and the corresponding subproblems solved by Frank-Wolfe, and alternative problem formulations to identify the situations in which each performs best. Our experiments evaluate the different approaches on instances from the Transportation Networks library and highlight the suitability of the mixed-integer Frank-Wolfe algorithm for this problem. In particular, we find that the Boscia framework is particularly applicable to this problem and that a mixed-integer linear Frank-Wolfe subproblem performs well for the deterministic case, while a penalty-based approach, with decoupled feasible regions for the design and flow variables, dominates other approaches for stochastic instances with many scenarios.},
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primaryclass = {math.OC},
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author = {Sharma, Kartikey and Hendrych, Deborah and Besançon, Mathieu and Pokutta, Sebastian},
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title = {Network Design for the Traffic Assignment Problem with Mixed-Integer {Frank-Wolfe}},
booktitle = {Proceedings of the Symposium on Experimental Algorithms},
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doi = {10.4230/LIPIcs.SEA.2024.16},
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archiveprefix = {arXiv},
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eprint = {2312.11200},
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abstract={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 the method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of the proposed method, especially on large and challenging instances.},
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primaryclass = {math.OC},
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author = {Hendrych, Deborah and Besançon, Mathieu and Pokutta, Sebastian},
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title = {Solving the Optimal Experiment Design Problem with Mixed-integer Convex Methods},
title="{{\"U}ber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt}",
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author={Albert Einstein},
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abstract={This is the abstract text.},
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journal={Ann. Phys.},
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volume={322},
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number={6},
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pages={132--148},
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year={1905},
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doi={10.1002/andp.19053220607},
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award={Albert Einstein receveid the **Nobel Prize in Physics** 1921 *for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect*},
author={Xiao, Wenjie and Hendrych, Deborah and Besan{\c{c}}on, Mathieu and Pokutta, Sebastian},
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archiveprefix = {arXiv},
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eprint = {2511.01479},
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primaryclass = {math.OC},
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abstract={ixed-integer nonlinear optimization (MINLP) comprises a large class of problems that are challenging to solve and exhibit a wide range of structures. The Boscia framework Hendrych et al. (2025b) focuses on convex MINLP where the nonlinearity appears in the objective only. This paper provides an overview of the framework and practical examples to illustrate its use and customizability. One key aspect is the integration and exploitation of Frank-Wolfe methods as continuous solvers within a branch-and-bound framework, enabling inexact node processing, warm-starting and explicit use of combinatorial structure among others. Three examples illustrate its flexibility, the user control over the optimization process and the benefit of oracle-based access to the objective and its gradient. The aim of this tutorial is to provide readers with an understanding of the main principles of the framework.},
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year={2025},
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pdf={https://arxiv.org/abs/2511.01479},
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abbr={preprint},
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bibtex_show={true},
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title={Letters on wave mechanics},
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author={Einstein, Albert and Schrödinger, Erwin and Planck, Max and Lorentz, Hendrik Antoon and Przibram, Karl},
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