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Related papers: The Frank-Wolfe algorithm: a short introduction

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How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this…

Machine Learning · Computer Science 2019-06-03 Mingrui Zhang , Lin Chen , Aryan Mokhtari , Hamed Hassani , Amin Karbasi

The Frank-Wolfe algorithm has regained much interest in its use in structurally constrained machine learning applications. However, one major limitation of the Frank-Wolfe algorithm is the slow local convergence property due to the…

Optimization and Control · Mathematics 2022-10-18 Zhaoyue Chen , Yifan Sun

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard…

Machine Learning · Computer Science 2019-02-01 Jarrid Rector-Brooks , Jun-Kun Wang , Barzan Mozafari

Frank-Wolfe methods are popular for optimization over a polytope. One of the reasons is because they do not need projection onto the polytope but only linear optimization over it. To understand its complexity, Lacoste-Julien and Jaggi…

Data Structures and Algorithms · Computer Science 2020-11-26 Luis Rademacher , Chang Shu

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

Optimization and Control · Mathematics 2011-12-30 Martin Jaggi

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…

Optimization and Control · Mathematics 2025-10-21 Gioni Mexi , Deborah Hendrych , Sébastien Designolle , Mathieu Besançon , Sebastian Pokutta

Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data…

Optimization and Control · Mathematics 2021-06-21 Immanuel. M. Bomze , Francesco Rinaldi , Damiano Zeffiro

In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first…

Optimization and Control · Mathematics 2022-06-20 Baojian Zhou , Yifan Sun

We consider the problem of minimizing a difference of (smooth) convex functions over a compact convex feasible region $P$, i.e., $\min_{x \in P} f(x) - g(x)$, with smooth $f$ and Lipschitz continuous $g$. This computational study builds…

Optimization and Control · Mathematics 2025-08-05 Sebastian Pokutta

Federated learning (FL) has gained a lot of attention in recent years for building privacy-preserving collaborative learning systems. However, FL algorithms for constrained machine learning problems are still limited, particularly when the…

Machine Learning · Computer Science 2024-08-20 Ali Dadras , Sourasekhar Banerjee , Karthik Prakhya , Alp Yurtsever

Optimal transport (OT), which provides a distance between two probability distributions by considering their spatial locations, has been applied to widely diverse applications. Computing an OT problem requires solution of linear programming…

Machine Learning · Computer Science 2021-03-11 Takumi Fukunaga , Hiroyuki Kasai

Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduce random-subspace Frank--Wolfe (RSFW), the first…

Optimization and Control · Mathematics 2026-05-26 Pierre-Louis Poirion , Sebastian Pokutta , Akiko Takeda

We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given…

Optimization and Control · Mathematics 2025-11-05 Dan Garber

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

Optimization and Control · Mathematics 2024-06-07 Wei Jiang , Sifan Yang , Wenhao Yang , Yibo Wang , Yuanyu Wan , Lijun Zhang

In this paper, we provide a sub-gradient based algorithm to solve general constrained convex optimization without taking projections onto the domain set. The well studied Frank-Wolfe type algorithms also avoid projections. However, they are…

Optimization and Control · Mathematics 2023-06-16 Kamiar Asgari , Michael J. Neely

We present new results for the Frank-Wolfe method (also known as the conditional gradient method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple…

Optimization and Control · Mathematics 2014-06-03 Robert M. Freund , Paul Grigas

Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy $\gamma_t =…

Optimization and Control · Mathematics 2024-04-09 Alejandro Carderera , Mathieu Besançon , Sebastian Pokutta

This paper aims to enhance the use of the Frank-Wolfe (FW) algorithm for training deep neural networks. Similar to any gradient-based optimization algorithm, FW suffers from high computational and memory costs when computing gradients for…

Machine Learning · Computer Science 2024-12-30 M. Rostami , S. S. Kia

We propose the pivoting meta algorithm (PM) to enhance optimization algorithms that generate iterates as convex combinations of vertices of a feasible region $C\subseteq \mathbb{R}^n$, including Frank-Wolfe (FW) variants. PM guarantees that…

Optimization and Control · Mathematics 2025-08-06 Elias Wirth , Mathieu Besançon , Sebastian Pokutta

We propose a semi-stochastic Frank-Wolfe algorithm with away-steps for regularized empirical risk minimization and extend it to problems with block-coordinate structure. Our algorithms use adaptive step-size and we show that they converge…

Optimization and Control · Mathematics 2016-02-16 Donald Goldfarb , Garud Iyengar , Chaoxu Zhou