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Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…

Optimization and Control · Mathematics 2016-02-26 Patrick L. Combettes , Jean-Christophe Pesquet

We consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators,…

Optimization and Control · Mathematics 2016-04-18 Meng Wen , Yu-Chao Tang , Jigen Peng

In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…

Optimization and Control · Mathematics 2017-01-25 Xiang Gao , Yangyang Xu , Shuzhong Zhang

We tackle highly nonconvex, nonsmooth composite optimization problems whose objectives comprise a Moreau-Yosida regularized term. Classical nonconvex proximal splitting algorithms, such as nonconvex ADMM, suffer from lack of convergence for…

Optimization and Control · Mathematics 2018-02-28 Emanuel Laude , Tao Wu , Daniel Cremers

We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…

Optimization and Control · Mathematics 2023-07-19 Renbo Zhao

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…

Optimization and Control · Mathematics 2020-03-17 César A. Uribe , Soomin Lee , Alexander Gasnikov , Angelia Nedić

We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…

Optimization and Control · Mathematics 2025-10-24 Matthias J. Ehrhardt , Subhadip Mukherjee , Hok Shing Wong

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

Optimization and Control · Mathematics 2021-04-20 Yuzixuan Zhu , Deyi Liu , Quoc Tran-Dinh

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

Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In…

Optimization and Control · Mathematics 2025-04-16 Pedro Pérez-Aros , David Torregrosa-Belén

Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…

We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a…

Optimization and Control · Mathematics 2020-09-25 Stanislav Mazurenko , Jyrki Jauhiainen , Tuomo Valkonen

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

Optimization and Control · Mathematics 2015-03-04 Quoc Tran-Dinh , Volkan Cevher

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…

Optimization and Control · Mathematics 2022-02-22 Francisco J. Aragón-Artacho , Radu I. Boţ , David Torregrosa-Belén

This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…

Optimization and Control · Mathematics 2020-07-14 Xiuxian Li , Gang Feng , Lihua Xie

Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal-dual algorithm, in which the dual update is randomized;…

Optimization and Control · Mathematics 2023-03-08 Laurent Condat , Peter Richtárik

This work proposes an Accelerated Primal-Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form min f(x) + g(Bx), where g is nonsmooth and B is a linear operator. The APDFP features…

Optimization and Control · Mathematics 2025-11-04 Ya-Nan Zhu

Under consideration are multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling terms penalizing linear mixtures of the components. We…

Optimization and Control · Mathematics 2021-08-27 Minh N. Bùi , Patrick L. Combettes , Zev C. Woodstock

This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the…

Optimization and Control · Mathematics 2024-04-17 Puya Latafat , Andreas Themelis , Panagiotis Patrinos

The Langevin algorithms are frequently used to sample the posterior distributions in Bayesian inference. In many practical problems, however, the posterior distributions often consist of non-differentiable components, posing challenges for…

Numerical Analysis · Mathematics 2023-04-11 Ziruo Cai , Jinglai Li , Xiaoqun Zhang