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We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…

Optimization and Control · Mathematics 2024-07-08 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

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

In this paper, we focus on solving a distributed convex aggregative optimization problem in a network, where each agent has its own cost function which depends not only on its own decision variables but also on the aggregated function of…

Optimization and Control · Mathematics 2022-07-26 Tongyu Wang , Peng Yi

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

Optimization and Control · Mathematics 2011-12-30 Martin Jaggi

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Machine Learning · Computer Science 2018-02-02 Tianyi Lin , Linbo Qiao , Teng Zhang , Jiashi Feng , Bofeng Zhang

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh

Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…

Artificial Intelligence · Computer Science 2023-07-19 Yunwen Lei

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 consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…

Optimization and Control · Mathematics 2022-10-27 Dan Garber , Ron Fisher

We consider two greedy algorithms for minimizing a convex function in a bounded convex set: an algorithm by Jones [1992] and the Frank-Wolfe (FW) algorithm. We first consider approximate versions of these algorithms. For smooth convex…

Optimization and Control · Mathematics 2018-11-19 Nan Ye , Peter Bartlett

Differentiable optimization has received a significant amount of attention due to its foundational role in the domain of machine learning based on neural networks. This paper proposes a differentiable layer, named Differentiable Frank-Wolfe…

Machine Learning · Computer Science 2024-04-01 Zixuan Liu , Liu Liu , Xueqian Wang , Peilin Zhao

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

In this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of…

Machine Learning · Computer Science 2016-06-01 Anton Osokin , Jean-Baptiste Alayrac , Isabella Lukasewitz , Puneet K. Dokania , Simon Lacoste-Julien

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

This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem…

Methodology · Statistics 2024-11-05 Giorgio Micali , Clement Lezane , Annika Betken

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration,…

Optimization and Control · Mathematics 2020-12-11 Bingcong Li , Lingda Wang , Georgios B. Giannakis , Zhizhen Zhao

Owing to their low-complexity iterations, Frank-Wolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity…

Optimization and Control · Mathematics 2017-11-22 Liang Zhang , Gang Wang , Daniel Romero , Georgios B. Giannakis

We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…

Optimization and Control · Mathematics 2013-03-12 Nicolas Le Roux , Mark Schmidt , Francis Bach

The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe in 1956 was so well received by the community that new algorithms (also called Frank--Wolfe type algorithms) are still being actively created. In this paper, we…

Optimization and Control · Mathematics 2023-05-26 Aleksandr Lobanov , Anton Anikin , Alexander Gasnikov , Alexander Gornov , Sergey Chukanov