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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

We give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of $O(1/\sqrt{t})$ on non-convex objectives with a Lipschitz continuous gradient. Our analysis is affine invariant and is the first, to the best of…

Optimization and Control · Mathematics 2016-07-07 Simon Lacoste-Julien

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

This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these…

Optimization and Control · Mathematics 2023-02-28 P. B. Assunção , O. P. Ferreira , L. F. Prudente

We propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality…

Machine Learning · Computer Science 2013-01-15 Simon Lacoste-Julien , Martin Jaggi , Mark Schmidt , Patrick Pletscher

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 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

This paper considers distributed stochastic optimization, in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network. Stochastic…

Optimization and Control · Mathematics 2022-08-09 Jie Hou , Xianlin Zeng , Gang Wang , Jian Sun , Jie Chen

We propose a simple variant of the generalized Frank-Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on the dual variables. We show that in this variant, one can choose a…

Optimization and Control · Mathematics 2022-10-27 Renbo Zhao , Qiuyun Zhu

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

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…

Optimization and Control · Mathematics 2022-05-25 Zeeshan Akhtar , Ketan Rajawat

The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are…

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

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 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

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

We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject…

Optimization and Control · Mathematics 2018-06-05 Xiaohan Wei , Michael J. Neely

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

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 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