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An extension of the Frank-Wolfe Algorithm (FWA), also known as Conditional Gradient algorithm, is proposed. In its standard form, the FWA allows to solve constrained optimization problems involving $\beta$-smooth cost functions, calling at…

Optimization and Control · Mathematics 2024-03-28 Guilherme Mazanti , Thibault Moquet , Laurent Pfeiffer

The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a compact convex set $\mathcal{C}$. While many convergence results have been derived in terms of function values, hardly nothing is known about…

Optimization and Control · Mathematics 2022-02-18 Jérôme Bolte , Cyrille W. Combettes , Édouard Pauwels

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 analyze gradient-free methods with one-point feedback for stochastic saddle point problems $\min_{x}\max_{y} \varphi(x, y)$. For non-smooth and smooth cases, we present analysis in a general geometric setup with arbitrary…

Optimization and Control · Mathematics 2022-09-12 Aleksandr Beznosikov , Vasilii Novitskii , Alexander Gasnikov

In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…

Machine Learning · Statistics 2018-02-19 Lin Chen , Hamed Hassani , Amin Karbasi

We introduce a few variants on Frank-Wolfe style algorithms suitable for large scale optimization. We show how to modify the standard Frank-Wolfe algorithm using stochastic gradients, approximate subproblem solutions, and sketched decision…

Optimization and Control · Mathematics 2018-08-17 Lijun Ding , Madeleine Udell

Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…

Optimization and Control · Mathematics 2023-09-12 Morteza Boroun , Zeinab Alizadeh , Afrooz Jalilzadeh

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

Optimization and Control · Mathematics 2025-05-02 Michael Muehlebach , Michael I. Jordan

In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…

Optimization and Control · Mathematics 2025-03-25 Anteneh Getachew Gebrie , Ellen Hidemi Fukuda

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 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

Frank-Wolfe algorithms (FW) are popular first-order methods for solving constrained convex optimization problems that rely on a linear minimization oracle instead of potentially expensive projection-like oracles. Many works have identified…

Optimization and Control · Mathematics 2023-09-18 Elias Wirth , Thomas Kerdreux , Sebastian Pokutta

In the context of gridless sparse optimization, the Sliding Frank Wolfe algorithm recently introduced has shown interesting analytical and practical properties. Nevertheless, is application to large data, such as in the case of 3D…

Image and Video Processing · Electrical Eng. & Systems 2020-09-14 Jean-Baptiste Courbot , Bruno Colicchio

Differentiable optimization has received a significant amount of attention due to its foundational role in the domain of machine learning based on neural networks. This paper proposes a differentiable layer, named Differentiable Frank-Wolfe…

Machine Learning · Computer Science 2024-04-01 Zixuan Liu , Liu Liu , Xueqian Wang , Peilin Zhao

We study the convergence properties of the original and away-step Frank-Wolfe algorithms for linearly constrained stochastic optimization assuming the availability of unbiased objective function gradient estimates. The objective function is…

Optimization and Control · Mathematics 2025-04-08 Natthawut Boonsiriphatthanajaroen , Shane G. Henderson

We tackle robust optimization problems under objective uncertainty in the oracle model, i.e., when the deterministic problem is solved by an oracle. The oracle-based setup is favorable in many situations, e.g., when a compact formulation of…

Optimization and Control · Mathematics 2024-12-06 Mathieu Besançon , Jannis Kurtz

An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective's gradient…

Optimization and Control · Mathematics 2026-04-01 S. Gratton , Ph. L. Toint

We study the convergence properties of the 'greedy' Frank-Wolfe algorithm with a unit step size, for a convex maximization problem over a compact set. We assume the function satisfies smoothness and strong convexity. These assumptions…

Optimization and Control · Mathematics 2025-05-02 Fatih Selim Aktas , Christian Kroer

This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…

Optimization and Control · Mathematics 2022-07-28 Kunal Garg , Mayank Baranwal

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