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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

In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…

Optimization and Control · Mathematics 2020-09-10 Hamed Hassani , Amin Karbasi , Aryan Mokhtari , Zebang Shen

The Frank-Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently received much attention in the optimization and machine…

Optimization and Control · Mathematics 2024-01-19 Liaoyuan Zeng , Yongle Zhang , Guoyin Li , Ting Kei Pong , Xiaozhou Wang

Muon is a recently proposed optimizer that enforces orthogonality in parameter updates by projecting gradients onto the Stiefel manifold, leading to stable and efficient training in large-scale deep neural networks. Meanwhile, the…

Machine Learning · Computer Science 2026-03-18 Hideaki Iiduka

While adaptive gradient methods are the workhorse of modern machine learning, sign-based optimization algorithms such as Lion and Muon have recently demonstrated superior empirical performance over AdamW in training large language models…

Machine Learning · Computer Science 2026-05-11 Dingzhi Yu , Hongyi Tao , Yuanyu Wan , Luo Luo , Lijun Zhang

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

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

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

Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient…

Machine Learning · Statistics 2018-06-15 Lin Chen , Christopher Harshaw , Hamed Hassani , Amin Karbasi

Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While…

Optimization and Control · Mathematics 2021-10-20 Thomas Kerdreux , Alexandre d'Aspremont , Sebastian Pokutta

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

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

The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known…

Optimization and Control · Mathematics 2015-11-19 Simon Lacoste-Julien , Martin Jaggi

Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as…

Machine Learning · Statistics 2015-10-27 Emanuele Frandi , Ricardo Nanculef , Johan Suykens

We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our…

Optimization and Control · Mathematics 2025-12-01 Hoomaan Maskan , Yikun Hou , Suvrit Sra , Alp Yurtsever

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

Recent optimizers such as Lion and Muon have demonstrated strong empirical performance by normalizing gradient momentum via linear minimization oracles (LMOs). While variance reduction has been explored to accelerate LMO-based methods, it…

Machine Learning · Computer Science 2026-05-08 Won-Jun Jang , Si-Hyeon Lee

The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it…

Optimization and Control · Mathematics 2015-08-17 Dan Garber , Elad Hazan

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

The Frank-Wolfe (FW) method is a popular algorithm for solving large-scale convex optimization problems appearing in structured statistical learning. However, the traditional Frank-Wolfe method can only be applied when the feasible region…

Optimization and Control · Mathematics 2021-10-11 Haoyue Wang , Haihao Lu , Rahul Mazumder