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This paper focuses on the problem of \emph{constrained} \emph{stochastic} optimization. A zeroth order Frank-Wolfe algorithm is proposed, which in addition to the projection-free nature of the vanilla Frank-Wolfe algorithm makes it gradient…

Optimization and Control · Mathematics 2019-02-20 Anit Kumar Sahu , Manzil Zaheer , Soummya Kar

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 investigate a class of nonconvex optimization problems characterized by a feasible set consisting of level-bounded nonconvex regularizers, with a continuously differentiable objective. We propose a novel hybrid approach to tackle such…

Optimization and Control · Mathematics 2024-10-28 Xiangyu Yang , Hao Wang , Yichen Zhu , Xiao Wang

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

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

A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers…

Optimization and Control · Mathematics 2019-10-30 Francesco Locatello , Alp Yurtsever , Olivier Fercoq , Volkan Cevher

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

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

Error bound condition has recently gained revived interest in optimization. It has been leveraged to derive faster convergence for many popular algorithms, including subgradient methods, proximal gradient method and accelerated proximal…

Optimization and Control · Mathematics 2018-10-12 Yi Xu , Tianbao Yang

Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data…

Optimization and Control · Mathematics 2021-06-21 Immanuel. M. Bomze , Francesco Rinaldi , Damiano Zeffiro

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

We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization…

The Frank-Wolfe algorithm achieves a convergence rate of $\mathcal{O}(1/T)$ for smooth convex optimization over compact convex domains, accelerating to $\mathcal{O}(1/T^2)$ when both the objective and the feasible set are strongly convex.…

Optimization and Control · Mathematics 2026-05-19 Jannis Halbey , Christophe Roux , Sebastian Pokutta

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

We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors…

Optimization and Control · Mathematics 2020-08-18 Lijun Ding , Yingjie Fei , Qiantong Xu , Chengrun Yang

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

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

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 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 study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical complexity bounds to certain non-convex functions, we focus on the class of…

Optimization and Control · Mathematics 2025-07-24 R. Diaz Millan , Orizon Pereira Ferreira , Julien Ugon