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Related papers: Accelerated Frank-Wolfe Algorithms: Complementarit…

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The Frank-Wolfe method and its extensions are well-suited for delivering solutions with desirable structural properties, such as sparsity or low-rank structure. We introduce a new variant of the Frank-Wolfe method that combines Frank-Wolfe…

Optimization and Control · Mathematics 2019-06-11 Paul Grigas , Alfonso Lobos , Nathan Vermeersch

In this paper we provide an introduction to the Frank-Wolfe algorithm, a method for smooth convex optimization in the presence of (relatively) complicated constraints. We will present the algorithm, introduce key concepts, and establish…

Optimization and Control · Mathematics 2023-11-30 Sebastian Pokutta

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

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

Optimization and Control · Mathematics 2026-02-19 Shota Takahashi , Sebastian Pokutta , Akiko Takeda

The Frank-Wolfe algorithm has become a popular first-order optimization algorithm for it is simple and projection-free, and it has been successfully applied to a variety of real-world problems. Its main drawback however lies in its…

Optimization and Control · Mathematics 2020-06-25 Cyrille W. Combettes , Sebastian Pokutta

Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been…

Computer Vision and Pattern Recognition · Computer Science 2015-10-27 Hector Allende , Emanuele Frandi , Ricardo Nanculef , Claudio Sartori

Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or…

Optimization and Control · Mathematics 2018-04-11 Gauthier Gidel , Fabian Pedregosa , Simon Lacoste-Julien

The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by…

Optimization and Control · Mathematics 2024-09-17 Aleksandr Beznosikov , David Dobre , Gauthier Gidel

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 present and analyze a new generalized Frank-Wolfe method for the composite optimization problem $(P):{\min}_{x\in\mathbb{R}^n}\; f(\mathsf{A} x) + h(x)$, where $f$ is a $\theta$-logarithmically-homogeneous self-concordant barrier,…

Optimization and Control · Mathematics 2021-12-07 Renbo Zhao , Robert M. Freund

We present a new Frank-Wolfe (FW) type algorithm that is applicable to minimization problems with a nonsmooth convex objective. We provide convergence bounds and show that the scheme yields so-called coreset results for various Machine…

Optimization and Control · Mathematics 2017-08-23 Sathya N. Ravi , Maxwell D. Collins , Vikas Singh

Maximizing a DR-submodular function subject to a general convex set is an NP-hard problem arising from many applications in combinatorial optimization and machine learning. While it is highly desirable to design efficient approximation…

Data Structures and Algorithms · Computer Science 2022-03-29 Donglei Du , Zhicheng Liu , Chenchen Wu , Dachuan Xu , Yang Zhou

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling…

Optimization and Control · Mathematics 2018-08-29 Hoi-To Wai , Jean Lafond , Anna Scaglione , Eric Moulines

We consider the problem of minimizing the sum of two convex functions. One of those functions has Lipschitz-continuous gradients, and can be accessed via stochastic oracles, whereas the other is "simple". We provide a Bregman-type algorithm…

Optimization and Control · Mathematics 2024-11-26 Benjamin Dubois-Taine , Francis Bach , Quentin Berthet , Adrien Taylor

We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ primal-gap barrier in the general smooth…

Optimization and Control · Mathematics 2026-05-05 Sebastian Pokutta

We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block…

Machine Learning · Computer Science 2019-06-07 Qi Lei , Jiacheng Zhuo , Constantine Caramanis , Inderjit S. Dhillon , Alexandros G. Dimakis

The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…

Optimization and Control · Mathematics 2021-06-15 Cyrille W. Combettes , Sebastian Pokutta

This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or…

Numerical Analysis · Mathematics 2018-11-16 Quentin Denoyelle , Vincent Duval , Gabriel Peyré , Emmanuel Soubies

We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as…

Optimization and Control · Mathematics 2023-07-20 Timo Kreimeier , Sebastian Pokutta , Andrea Walther , Zev Woodstock

We propose a novel generalization of the conditional gradient (CG / Frank-Wolfe) algorithm for minimizing a smooth function $f$ under an intersection of compact convex sets, using a first-order oracle for $\nabla f$ and linear minimization…

Optimization and Control · Mathematics 2024-10-11 Zev Woodstock , Sebastian Pokutta