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The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…

Optimization and Control · Mathematics 2019-11-12 Daniel Reem , Simeon Reich , Alvaro De Pierro

This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…

Optimization and Control · Mathematics 2018-03-28 Emanuel Laude , Daniel Cremers

In the applications of signal processing and data analytics, there is a wide class of non-convex problems whose objective function is freed from the common global Lipschitz continuous gradient assumption (e.g., the nonnegative matrix…

Optimization and Control · Mathematics 2019-12-17 Tianxiang Gao , Songtao Lu , Jia Liu , Chris Chu

We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We show that the…

Functional Analysis · Mathematics 2018-11-26 Szilárd Csaba László

In this work, we introduce a unifying Bregman-based majorization-minimization (MM) framework for solving nonconvex nonsmooth optimization problems. The proposed approach leverages Bregman divergences, possibly varying across iterations, to…

Optimization and Control · Mathematics 2026-04-15 Maxence Adly , Alix Chazottes , Emilie Chouzenoux , Jean-Christophe Pesquet , Florent Sureau

We introduce two algorithms for nonconvex regularized finite sum minimization, where typical Lipschitz differentiability assumptions are relaxed to the notion of relative smoothness. The first one is a Bregman extension of Finito/MISO,…

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

We propose an extension of a special form of gradient descent -- in the literature known as linearised Bregman iteration -- to a larger class of non-convex functions. We replace the classical (squared) two norm metric in the gradient…

Optimization and Control · Mathematics 2021-05-26 Martin Benning , Marta M. Betcke , Matthias J. Ehrhardt , Carola-Bibiane Schönlieb

This work proposes an efficient batch algorithm for feature selection in reinforcement learning (RL) with theoretical convergence guarantees. To mitigate the estimation bias inherent in conventional regularization schemes, the first…

Machine Learning · Computer Science 2025-09-22 Kyohei Suzuki , Konstantinos Slavakis

Recently, adversarial imitation learning has shown a scalable reward acquisition method for inverse reinforcement learning (IRL) problems. However, estimated reward signals often become uncertain and fail to train a reliable statistical…

Machine Learning · Computer Science 2023-01-06 Dong-Sig Han , Hyunseo Kim , Hyundo Lee , Je-Hwan Ryu , Byoung-Tak Zhang

In this paper we develop a Bregman regularized proximal point algorithm for solving monotone equilibrium problems on Hadamard manifolds. It has been shown that the regularization term induced by a Bregman function is, in general, nonconvex…

Optimization and Control · Mathematics 2026-01-21 Shikher Sharma , Simeon Reich

The Bregman proximal gradient method (BPGM), which uses the Bregman distance as a proximity measure in the iterative scheme, has recently been re-developed for minimizing convex composite problems without the global Lipschitz gradient…

Optimization and Control · Mathematics 2025-04-16 Lei Yang , Kim-Chuan Toh

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

In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…

Optimization and Control · Mathematics 2024-11-27 O. S. Savchuk , M. S. Alkousa , A. S. Shushko , A. A. Vyguzov , F. S. Stonyakin , D. A. Pasechnyuk , A. V. Gasnikov

The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for…

Optimization and Control · Mathematics 2023-07-31 Dirk A. Lorenz , Maximilian Winkler

In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain…

Optimization and Control · Mathematics 2025-04-03 Lionel Tondji , Dirk A. Lorenz , Ion Necoara

We discuss a special form of gradient descent that in the literature has become known as the so-called linearised Bregman iteration. The idea is to replace the classical (squared) two norm metric in the gradient descent setting with a…

Optimization and Control · Mathematics 2016-12-28 Martin Benning , Marta M. Betcke , Matthias J. Ehrhardt , Carola-Bibiane Schönlieb

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…

Optimization and Control · Mathematics 2021-06-30 Xin He , Rong Hu , Ya-Ping Fang

The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…

Optimization and Control · Mathematics 2019-11-11 Lorenzo Stella , Andreas Themelis , Panagiotis Patrinos

We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…

Optimization and Control · Mathematics 2017-06-21 Jérôme Bolte , Shoham Sabach , Marc Teboulle , Yakov Vaisbourd

In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of…

Numerical Analysis · Mathematics 2023-02-16 Silvia Bonettini , Peter Ochs , Marco Prato , Simone Rebegoldi