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Related papers: Proximal gradient methods beyond monotony

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In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Optimization and Control · Mathematics 2025-04-21 Spyridon Pougkakiotis , Dionysios S. Kalogerias

We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…

Optimization and Control · Mathematics 2026-03-16 Zepeng Wang , Juan Peypouquet

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

Optimization and Control · Mathematics 2015-04-24 A. S. Lewis , S. J. Wright

The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…

Optimization and Control · Mathematics 2021-01-01 Yuchen Xie , Raghu Bollapragada , Richard Byrd , Jorge Nocedal

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

Optimization and Control · Mathematics 2022-03-02 Boris S. Mordukhovich , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…

Optimization and Control · Mathematics 2023-07-19 Eduard Gorbunov , Adrien Taylor , Samuel Horváth , Gauthier Gidel

We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…

Optimization and Control · Mathematics 2026-04-16 Javier I. Madariaga

This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…

Optimization and Control · Mathematics 2024-01-10 I. Necoara , F. Chorobura

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

Optimization and Control · Mathematics 2024-09-26 Gregorio M. Sempere , Welington de Oliveira , Johannes O. Royset

We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…

Optimization and Control · Mathematics 2025-06-09 Keita Kume , Isao Yamada

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

Optimization and Control · Mathematics 2019-03-26 Jérôme Bolte , Zheng Chen , Edouard Pauwels

We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…

Optimization and Control · Mathematics 2019-09-20 Hilal Asi , John C. Duchi

In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…

Machine Learning · Computer Science 2017-08-16 Hamed Hassani , Mahdi Soltanolkotabi , Amin Karbasi

Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…

Optimization and Control · Mathematics 2023-02-10 Gilles Bareilles , Franck Iutzeler , Jérôme Malick

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

Optimization and Control · Mathematics 2022-08-10 Johannes O. Royset

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

In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…

Optimization and Control · Mathematics 2024-01-09 Shanglin Liu , Lei Wang , Nachuan Xiao , Xin Liu

Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…

Optimization and Control · Mathematics 2023-02-09 Alberto De Marchi , Andreas Themelis

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

Optimization and Control · Mathematics 2023-12-05 Yurii Nesterov

In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not linked directly to any parametric problem class. However,…

Optimization and Control · Mathematics 2025-09-26 Yurii Nesterov