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We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…

Optimization and Control · Mathematics 2018-07-31 Nimit Nimana , Narin Petrot

We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to…

Optimization and Control · Mathematics 2020-11-30 Saverio Salzo , Silvia Villa

Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…

Machine Learning · Computer Science 2025-02-19 Artem Riabinin , Ahmed Khaled , Peter Richtárik

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…

Numerical Analysis · Computer Science 2018-06-11 Ganzhao Yuan , Wei-Shi Zheng , Li Shen , Bernard Ghanem

We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert…

Numerical Analysis · Mathematics 2009-11-13 Kristian Bredies

This work considers the nonconvex, nonsmooth problem of minimizing a composite objective of the form $f(g(x))+h(x)$ where the inner mapping $g$ is a smooth finite summation or expectation amenable to variance reduction. In such settings,…

Optimization and Control · Mathematics 2025-10-16 Yue Wu , Benjamin Grimmer

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

Optimization and Control · Mathematics 2026-04-20 Minh N. Dao , Matthew K. Tam , Thang D. Truong

We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…

Optimization and Control · Mathematics 2019-10-23 Jinming Xu , Ying Sun , Ye Tian , Gesualdo Scutari

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

We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…

Optimization and Control · Mathematics 2013-06-25 Marc Lassonde , Ludovic Nagesseur

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Optimization and Control · Mathematics 2023-02-17 Jelena Diakonikolas , Cristóbal Guzmán

In this paper, we study large-scale convex optimization algorithms based on the Newton method applied to regularized generalized self-concordant losses, which include logistic regression and softmax regression. We first prove that our new…

Optimization and Control · Mathematics 2019-11-22 Ulysse Marteau-Ferey , Francis Bach , Alessandro Rudi

The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…

Optimization and Control · Mathematics 2024-02-19 Zhongzhu Chen , Marcia Fampa , Jon Lee

In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…

Optimization and Control · Mathematics 2024-02-29 Ewa Bednarczuk , Dirk Lorenz , The Hung Tran

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…

Machine Learning · Computer Science 2019-03-05 Azade Nazi , Will Hang , Anna Goldie , Sujith Ravi , Azalia Mirhoseini

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

Optimization and Control · Mathematics 2021-03-24 Nikita Doikov , Yurii Nesterov

We investigate the optimization aspects of personalized Federated Learning (FL). We propose general optimizers that can be applied to numerous existing personalized FL objectives, specifically a tailored variant of Local SGD and variants of…

Machine Learning · Computer Science 2023-05-30 Filip Hanzely , Boxin Zhao , Mladen Kolar

Friedlander, Mac\^{e}do, and Pong recently introduced the projected polar proximal point algorithm (P4A) for solving optimization problems by using the closed perspective transforms of convex objectives. We analyse a generalization (GP4A)…

Optimization and Control · Mathematics 2022-01-25 Scott B. Lindstrom

We propose a simple variant of the generalized Frank-Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on the dual variables. We show that in this variant, one can choose a…

Optimization and Control · Mathematics 2022-10-27 Renbo Zhao , Qiuyun Zhu