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In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…

Optimization and Control · Mathematics 2016-02-01 Radu Ioan Bot , Ernö Robert Csetnek

In this paper we aim to minimize the sum of two nonsmooth (possibly also nonconvex) functions in separate variables connected by a smooth coupling function. To tackle this problem we chose a continuous forward-backward approach and…

Optimization and Control · Mathematics 2020-01-29 Radu Ioan Bot , Laura Kanzler

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

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

In this paper, we study a class of fractional optimization problems, in which the numerator of the objective is the sum of a convex function and a differentiable function with a Lipschitz continuous gradient, while the denominator is a…

Optimization and Control · Mathematics 2025-04-16 Lei Yang , Xiangrui Kong , Min Zhang , Yaohua Hu

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method…

Optimization and Control · Mathematics 2015-03-24 Zhaosong Lu , Lin Xiao

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

This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Pierre Moulin

We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…

Optimization and Control · Mathematics 2020-03-26 D. Russell Luke , Yura Malitsky

We introduce a proximal limited--memory quasi--Newton scheme for minimizing the sum of a continuously differentiable function and a proper, lower semicontinuous and prox-bounded, possibly nonsmooth, function. Both functions might be…

Optimization and Control · Mathematics 2026-05-13 Simeon vom Dahl , Alberto De Marchi , Christian Kanzow

In this paper, we consider a class of structured nonsmooth optimization problems over an embedded submanifold of a Euclidean space, where the first part of the objective is the sum of a difference-of-convex (DC) function and a smooth…

Optimization and Control · Mathematics 2025-11-07 Qia Li , Na Zhang , Junyu Feng , Hanwei Yan

Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this…

Optimization and Control · Mathematics 2025-10-15 Cody Melcher , Zeinab Alizadeh , Lindsey Hiett , Afrooz Jalilzadeh , Erfan Yazdandoost Hamedani

In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The algorithm iPiano combines forward-backward splitting with an…

Computer Vision and Pattern Recognition · Computer Science 2014-04-21 Peter Ochs , Yunjin Chen , Thomas Brox , Thomas Pock

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…

Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are…

Optimization and Control · Mathematics 2026-03-10 Yuchen Li , Laura Balzano , Deanna Needell , Hanbaek Lyu

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

Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…

Machine Learning · Computer Science 2023-08-28 Yan Li , Caleb Ju , Ethan X. Fang , Tuo Zhao

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

Optimization and Control · Mathematics 2016-10-28 Jingwei Liang , Jalal Fadili , Gabriel Peyré

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Optimization and Control · Mathematics 2016-08-18 Qia Li , Yuesheng Xu , Na Zhang

Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix…

Optimization and Control · Mathematics 2020-12-25 Mahesh Chandra Mukkamala , Jalal Fadili , Peter Ochs