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We study Frank-Wolfe (FW) methods for constrained bilevel optimization when the lower-level problem is solved only approximately, yielding biased and inexact hypergradients. We analyze inexact variants of vanilla FW as well as away-step and…

Optimization and Control · Mathematics 2026-02-27 Anthony Palmieri , Francesco Rinaldi , Saverio Salzo , Sara Venturini

This paper proposes a new variant of Frank-Wolfe (FW), called $k$FW. Standard FW suffers from slow convergence: iterates often zig-zag as update directions oscillate around extreme points of the constraint set. The new variant, $k$FW,…

Optimization and Control · Mathematics 2021-11-17 Lijun Ding , Jicong Fan , Madeleine Udell

Deep neural networks is today one of the most popular choices in classification, regression and function approximation. However, the training of such deep networks is far from trivial as there are often millions of parameters to tune.…

Machine Learning · Computer Science 2020-06-09 Jakob Stigenberg

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 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

We study the linear convergence of variants of the Frank-Wolfe algorithms for some classes of strongly convex problems, using only affine-invariant quantities. As in Guelat & Marcotte (1986), we show the linear convergence of the standard…

Optimization and Control · Mathematics 2014-01-06 Simon Lacoste-Julien , Martin Jaggi

Frank-Wolfe methods are projection-free algorithms for constrained optimization whose practical performance often depends critically on the choice of step size. Classical closed-loop step-size rules typically require prior knowledge of a…

Optimization and Control · Mathematics 2026-05-29 Khanh-Hung Giang-Tran , Soroosh Shafiee , Nam Ho-Nguyen

We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight…

Optimization and Control · Mathematics 2026-05-21 Jannis Halbey , Seta Rakotomandimby , Mathieu Besançon , Sébastien Designolle , Sebastian Pokutta

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 address a large-scale and nonconvex optimization problem, involving an aggregative term. This term can be interpreted as the sum of the contributions of N agents to some common good, with N large. We investigate a relaxation of this…

Optimization and Control · Mathematics 2023-06-19 J. Frédéric Bonnans , Kang Liu , Nadia Oudjane , Laurent Pfeiffer , Cheng Wan

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

This paper studies the empirical efficacy and benefits of using projection-free first-order methods in the form of Conditional Gradients, a.k.a. Frank-Wolfe methods, for training Neural Networks with constrained parameters. We draw…

Machine Learning · Computer Science 2020-10-22 Sebastian Pokutta , Christoph Spiegel , Max Zimmer

We consider the problem of minimizing a smooth and convex function over the $n$-dimensional spectrahedron -- the set of real symmetric $n\times n$ positive semidefinite matrices with unit trace, which underlies numerous applications in…

Optimization and Control · Mathematics 2026-03-03 Dan Garber

The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper,…

Optimization and Control · Mathematics 2020-10-23 Cheng Chen , Luo Luo , Weinan Zhang , Yong Yu

Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a…

Optimization and Control · Mathematics 2015-11-09 Robert M. Freund , Paul Grigas , Rahul Mazumder

This paper is concerned with the Frank--Wolfe algorithm for a special class of {\it non-compact} constrained optimization problems. The notion of asymptotic cone is used to introduce this class of problems as well as to establish that the…

Optimization and Control · Mathematics 2021-09-29 O. P. Ferreira , W. S. Sosa

We study Frank-Wolfe algorithms - standard, pairwise, and away-steps - for efficient optimization of Dominant Set Clustering. We present a unified and computationally efficient framework to employ the different variants of Frank-Wolfe…

Machine Learning · Computer Science 2022-12-06 Carl Johnell , Morteza Haghir Chehreghani

It is known that the Frank-Wolfe (FW) algorithm, which is affine-covariant, enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring…

Optimization and Control · Mathematics 2020-11-09 Thomas Kerdreux , Lewis Liu , Simon Lacoste-Julien , Damien Scieur

We introduce regularized Frank-Wolfe, a general and effective algorithm for inference and learning of dense conditional random fields (CRFs). The algorithm optimizes a nonconvex continuous relaxation of the CRF inference problem using…

Machine Learning · Computer Science 2022-09-09 Đ. Khuê Lê-Huu , Karteek Alahari

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