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We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

Optimization and Control · Mathematics 2016-08-11 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

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

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…

Optimization and Control · Mathematics 2015-11-17 Guoyin Li , Ting Kei Pong

This paper studies a novel algorithm for nonconvex composite minimization which can be interpreted in terms of dual space nonlinear preconditioning for the classical proximal gradient method. The proposed scheme can be applied to additive…

Optimization and Control · Mathematics 2024-12-24 Emanuel Laude , Panagiotis Patrinos

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…

Numerical Analysis · Mathematics 2017-04-11 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato , Simone Rebegoldi

A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…

Machine Learning · Computer Science 2024-12-17 Naoki Sato , Koshiro Izumi , Hideaki Iiduka

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

We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this kind of problems can be classified into three classes.…

Optimization and Control · Mathematics 2019-05-14 Shixiang Chen , Shiqian Ma , Anthony Man-Cho So , Tong Zhang

We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…

Optimization and Control · Mathematics 2024-04-18 Yunier Bello-Cruz , J. G. Melo , L. F. Prudente , R. V. G. Serra

We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…

Optimization and Control · Mathematics 2018-12-04 Zhize Li , Jian Li

The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…

Optimization and Control · Mathematics 2016-02-08 Hideaki Iiduka

The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…

Numerical Analysis · Mathematics 2024-01-19 Abdeslem Hafid Bentbib , Khalide Jbilou , Ridwane Tahiri

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

Optimization and Control · Mathematics 2016-05-24 Sashank J. Reddi , Suvrit Sra , Barnabas Poczos , Alex Smola

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato

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

In this paper, we first introduce a preconditioned primal-dual gradient algorithm based on conjugate duality theory. This algorithm is designed to solve composite optimization problem whose objective function consists of two summands: a…

Optimization and Control · Mathematics 2023-09-27 Jiahong Guo , Xiao Wang , Xiantao Xiao

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

Optimization and Control · Mathematics 2019-12-05 Xiaokai Chang , Sanyang Liu , Jianchao Bai , Jun Yang

Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization…

Machine Learning · Statistics 2016-09-13 Xiyu Yu , Dacheng Tao