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This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…

Optimization and Control · Mathematics 2023-08-17 Vladimir Norkin , Alois Pichler , Anton Kozyriev

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 study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic…

Optimization and Control · Mathematics 2021-04-06 Melanie Weber , Suvrit Sra

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

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

In this paper, we consider Frank-Wolfe-based algorithms for composite convex optimization problems with objective involving a logarithmically-homogeneous, self-concordant functions. Recent Frank-Wolfe-based methods for this class of…

Optimization and Control · Mathematics 2023-10-24 Nimita Shinde , Vishnu Narayanan , James Saunderson

In this paper, we consider the problem of minimizing the average of a large number of nonsmooth and convex functions. Such problems often arise in typical machine learning problems as empirical risk minimization, but are computationally…

Machine Learning · Statistics 2018-05-21 Wenjie Huang

The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…

Optimization and Control · Mathematics 2021-06-15 Cyrille W. Combettes , Sebastian Pokutta

This paper is concerned with the Frank--Wolfe algorithm for a special class of {\it non-compact} constrained optimization problems. The notion of asymptotic cone is used to introduce this class of problems as well as to establish that the…

Optimization and Control · Mathematics 2021-09-29 O. P. Ferreira , W. S. Sosa

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…

Optimization and Control · Mathematics 2024-10-01 Tan Nhat Pham , Minh N. Dao , Rakibuzzaman Shah , Nargiz Sultanova , Guoyin Li , Syed Islam

We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…

Optimization and Control · Mathematics 2026-02-17 Zhihan Zhu , Yanhao Zhang , Yong Xia

Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is…

Optimization and Control · Mathematics 2020-06-30 Pavel Dvurechensky , Petr Ostroukhov , Kamil Safin , Shimrit Shtern , Mathias Staudigl

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

This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint…

Optimization and Control · Mathematics 2023-01-23 Xiaoyin Hu , Nachuan Xiao , Xin Liu , Kim-Chuan Toh

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

This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions,…

Machine Learning · Computer Science 2024-04-30 Mohammad Pedramfar , Yididiya Y. Nadew , Christopher J. Quinn , Vaneet Aggarwal

This paper aims to enhance the use of the Frank-Wolfe (FW) algorithm for training deep neural networks. Similar to any gradient-based optimization algorithm, FW suffers from high computational and memory costs when computing gradients for…

Machine Learning · Computer Science 2024-12-30 M. Rostami , S. S. Kia

One of the beauties of the projected gradient descent method lies in its rather simple mechanism and yet stable behavior with inexact, stochastic gradients, which has led to its wide-spread use in many machine learning applications.…

Optimization and Control · Mathematics 2019-10-11 Mingrui Zhang , Zebang Shen , Aryan Mokhtari , Hamed Hassani , Amin Karbasi

We investigate the robustness of the Frank-Wolfe method when gradients are computed inexactly and examine the relative computational cost of the linear minimization oracle (LMO) versus projection. For smooth nonconvex functions, we…

Optimization and Control · Mathematics 2026-01-27 Tao Hu

The Frank-Wolfe algorithm has become a popular first-order optimization algorithm for it is simple and projection-free, and it has been successfully applied to a variety of real-world problems. Its main drawback however lies in its…

Optimization and Control · Mathematics 2020-06-25 Cyrille W. Combettes , Sebastian Pokutta