English
Related papers

Related papers: Splitting the Conditional Gradient Algorithm

200 papers

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

Optimization and Control · Mathematics 2026-05-28 Yizun Lin , Jian-Feng Cai , Zhao-Rong Lai , Cheng Li

The analysis of projection-free first order methods is often complicated by the presence of different kinds of "good" and "bad" steps. In this article, we propose a unifying framework for projection-free methods, aiming to simplify the…

Optimization and Control · Mathematics 2020-08-25 Francesco Rinaldi , Damiano Zeffiro

We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component,…

Optimization and Control · Mathematics 2019-05-17 Lihua Lei , Cheng Ju , Jianbo Chen , Michael I. Jordan

We study Frank-Wolfe (FW) methods for constrained bilevel optimization when the lower-level problem is solved only approximately, yielding biased and inexact hypergradients. We analyze inexact variants of vanilla FW as well as away-step and…

Optimization and Control · Mathematics 2026-02-27 Anthony Palmieri , Francesco Rinaldi , Saverio Salzo , Sara Venturini

Recently the away-step Frank-Wolfe algoritm for constrained multiobjective optimization has been shown linear convergence rate over a polytope which is generated by finite points set. In this paper we design a decomposition-invariant…

Optimization and Control · Mathematics 2024-09-10 Zhuoxin Fan , Liping Tang

This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…

Machine Learning · Computer Science 2022-09-13 Srujan Teja Thomdapu , Harshvardhan , Ketan Rajawat

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

Optimization and Control · Mathematics 2025-05-02 Michael Muehlebach , Michael I. Jordan

We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that…

Optimization and Control · Mathematics 2015-04-21 Amir Beck , Shimrit Shtern

As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants…

Optimization and Control · Mathematics 2021-05-11 Mingrui Zhang

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

Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching…

Machine Learning · Computer Science 2017-03-08 Francesco Locatello , Rajiv Khanna , Michael Tschannen , Martin Jaggi

We analyze stochastic conditional gradient methods for constrained optimization problems arising in over-parametrized machine learning. We show that one could leverage the interpolation-like conditions satisfied by such models to obtain…

Optimization and Control · Mathematics 2022-01-28 Tesi Xiao , Krishnakumar Balasubramanian , Saeed Ghadimi

We prove that the block-coordinate Frank-Wolfe (BCFW) algorithm converges with state-of-the-art rates in both convex and nonconvex settings under a very mild "block-iterative" assumption. This appears to be the first result on BCFW…

Optimization and Control · Mathematics 2025-12-17 Gábor Braun , Jannis Halbey , Sebastian Pokutta , Zev Woodstock

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

Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…

Optimization and Control · Mathematics 2024-07-19 Deborah Hendrych , Hannah Troppens , Mathieu Besançon , Sebastian Pokutta

The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…

Optimization and Control · Mathematics 2024-11-01 Xiao Li , Lei Zhao , Daoli Zhu , Anthony Man-Cho So

We propose a projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization, where the objective function is a nested composition of $T$ functions and the constraint set is a closed convex…

Optimization and Control · Mathematics 2022-10-11 Tesi Xiao , Krishnakumar Balasubramanian , Saeed Ghadimi

The article proposes a Caputo fractional conjugate gradient (CFCG) method for unconstrained optimization problems which is applicable to smooth as well as non-smooth problmes. The proposed method uses a non-adaptive version of the Caputo…

Optimization and Control · Mathematics 2025-12-22 Barsha Shawa , Md Abu Talhamainuddin Ansary

This paper studies the asymptotic behavior of the constant step Stochastic Gradient Descent for the minimization of an unknown function F , defined as the expectation of a non convex, non smooth, locally Lipschitz random function. As the…

Numerical Analysis · Mathematics 2022-04-13 Pascal Bianchi , Walid Hachem , Sholom Schechtman

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…

Optimization and Control · Mathematics 2026-04-10 Huaiyi Mu , Yujie Tang , Jie Song , Zhongkui Li