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Related papers: Frank-Wolfe with a Nearest Extreme Point Oracle

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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

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

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

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard…

Machine Learning · Computer Science 2019-02-01 Jarrid Rector-Brooks , Jun-Kun Wang , Barzan Mozafari

We study a class of convex-concave saddle-point problems of the form $\min_x\max_y \langle Kx,y\rangle+f_{\cal{P}}(x)-h^\ast(y)$ where $K$ is a linear operator, $f_{\cal{P}}$ is the sum of a convex function $f$ with a Lipschitz-continuous…

Optimization and Control · Mathematics 2021-06-07 Vladimir Kolmogorov , Thomas Pock

Frank-Wolfe methods are popular for optimization over a polytope. One of the reasons is because they do not need projection onto the polytope but only linear optimization over it. To understand its complexity, Lacoste-Julien and Jaggi…

Data Structures and Algorithms · Computer Science 2020-11-26 Luis Rademacher , Chang Shu

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

Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…

Optimization and Control · Mathematics 2023-08-01 G. V. Aivazian , F. S. Stonyakin , D. A. Pasechnyuk , M. S. Alkousa , A. M. Raigorodskii

The minimum volume enclosing ellipsoid (MVEE) problem is an optimization problem in the basis of many practical problems. This paper describes some new properties of this model and proposes a first-order oracle algorithm, the Adjusted…

Optimization and Control · Mathematics 2018-04-03 Jie Tao , Wei Zhang , Chao Lu

We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…

Optimization and Control · Mathematics 2019-12-10 Ilnura Usmanova , Andreas Krause , Maryam Kamgarpour

Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a…

Optimization and Control · Mathematics 2015-11-09 Robert M. Freund , Paul Grigas , Rahul Mazumder

This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an…

Optimization and Control · Mathematics 2026-05-20 Julien Weibel , Pierre Gaillard , Wouter M. Koolen , Adrien Taylor

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 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 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

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

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 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

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

Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the…

Machine Learning · Computer Science 2018-06-27 Han Zhao , Geoff Gordon