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The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…

Optimization and Control · Mathematics 2021-10-20 Robin Francis , Sundeep Prabhakar Chepuri

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

We present and analyze an away-step Frank-Wolfe method for the convex optimization problem ${\min}_{x\in\mathcal{X}} \; f(\mathsf{A} x) + \langle{c},{x}\rangle$, where $f$ is a $\theta$-logarithmically-homogeneous self-concordant barrier,…

Optimization and Control · Mathematics 2023-08-30 Renbo Zhao

This paper analyzes the convergence rates of the {\it Frank-Wolfe } method for solving convex constrained multiobjective optimization. We establish improved convergence rates under different assumptions on the objective function, the…

Optimization and Control · Mathematics 2024-06-11 Douglas S. Gonçalves , Max L. N. Gonçalves , Jefferson G. Melo

The Frank-Wolfe algorithm is a popular method in structurally constrained machine learning applications, due to its fast per-iteration complexity. However, one major limitation of the method is a slow rate of convergence that is difficult…

Optimization and Control · Mathematics 2023-04-14 Zhaoyue Chen , Yifan Sun

We investigate variants of the Frank-Wolfe (FW) algorithm for smoothing and strongly convex optimization over polyhedral sets, with the goal of designing algorithms that achieve linear convergence while minimizing per-iteration complexity…

Optimization and Control · Mathematics 2025-09-30 Haoning Wang , Houduo Qi , Liping Zhang

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…

Optimization and Control · Mathematics 2022-05-25 Zeeshan Akhtar , Ketan Rajawat

The paper introduces a new adaptive version of the Frank-Wolfe algorithm for relatively smooth convex functions. It is proposed to use the Bregman divergence other than half the square of the Euclidean norm in the formula for step-size.…

Optimization and Control · Mathematics 2024-07-23 Alexander Vyguzov , Fedor Stonyakin

We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only…

Optimization and Control · Mathematics 2018-03-21 Thomas Kerdreux , Fabian Pedregosa , Alexandre d'Aspremont

Recent papers have shown that the Frank-Wolfe algorithm (FW) with open-loop step-sizes exhibits rates of convergence faster than the iconic $\mathcal{O}(t^{-1})$ rate. In particular, when the minimizer of a strongly convex function over a…

Optimization and Control · Mathematics 2025-01-22 Elias Wirth , Javier Pena , Sebastian Pokutta

Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the…

Machine Learning · Statistics 2018-03-22 Edward Cheung , Yuying Li

The analysis of Frank Wolfe (FW) variants is often complicated by the presence of different kinds of "good" and "bad" steps. In this article we aim to simplify the convergence analysis of some of these variants by getting rid of such a…

Optimization and Control · Mathematics 2022-11-22 Francesco Rinaldi , Damiano Zeffiro

The Frank-Wolfe algorithm, a very first optimization method and also known as the conditional gradient method, was introduced by Frank and Wolfe in 1956. Due to its simple linear subproblems, the Frank-Wolfe algorithm has recently been…

Optimization and Control · Mathematics 2017-10-23 Hong-Kun Xu

In the present paper, we formulate two versions of Frank--Wolfe algorithm or conditional gradient method to solve the DC optimization problem with an adaptive step size. The DC objective function consists of two components; the first is…

Optimization and Control · Mathematics 2026-02-02 R. Díaz Millán , O. P. Ferreira , J. Ugon

The Frank-Wolfe method solves smooth constrained convex optimization problems at a generic sublinear rate of $\mathcal{O}(1/T)$, and it (or its variants) enjoys accelerated convergence rates for two fundamental classes of constraints:…

Optimization and Control · Mathematics 2020-06-17 Thomas Kerdreux , Alexandre d'Aspremont , Sebastian Pokutta

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW…

Optimization and Control · Mathematics 2017-03-07 Gauthier Gidel , Tony Jebara , Simon Lacoste-Julien

Recently the away-step Frank-Wolfe algoritm for constrained multiobjective optimization has been shown linear convergence rate over a polytope which is generated by finite points set. In this paper we design a decomposition-invariant…

Optimization and Control · Mathematics 2024-09-10 Zhuoxin Fan , Liping Tang

We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their…

Optimization and Control · Mathematics 2016-08-01 Sashank J. Reddi , Suvrit Sra , Barnabas Poczos , Alex Smola

We provide a template to derive convergence rates for the following popular versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe, Frank-Wolfe with away steps, Frank-Wolfe with blended pairwise steps, and Frank-Wolfe with…

Optimization and Control · Mathematics 2025-05-21 Elias Wirth , Javier Pena , Sebastian Pokutta

We consider variants of the classical Frank-Wolfe algorithm for constrained smooth convex minimization, that instead of access to the standard oracle for minimizing a linear function over the feasible set, have access to an oracle that can…

Optimization and Control · Mathematics 2022-02-10 Dan Garber , Noam Wolf