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We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…

Optimization and Control · Mathematics 2026-03-16 Zepeng Wang , Juan Peypouquet

We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…

Optimization and Control · Mathematics 2022-03-29 Hui Ouyang

The Alternating Minimization Algorithm (AMA) has been proposed by Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be…

Optimization and Control · Mathematics 2018-06-04 Sandy Bitterlich , Radu Ioan Bot , Ernö Robert Csetnek , Gert Wanka

Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…

Optimization and Control · Mathematics 2019-01-08 Hong-Kun Xu , Vera Roshchina

The classical Krasnoselskii-Mann iteration is broadly used for approximating fixed points of nonexpansive operators. To accelerate the convergence of the Krasnoselskii-Mann iteration, the inertial methods were received much attention in…

Functional Analysis · Mathematics 2020-01-09 Fuying Cui , Yang Yang , Yuchao Tang , Chuanxi Zhu

In this paper, we consider a non-convex problem which is the sum of $\ell_0$-norm and a convex smooth function under box constraint. We propose one proximal iterative hard thresholding type method with extrapolation step used for…

Optimization and Control · Mathematics 2018-01-03 Xue Zhang , Xiaoqun Zhang

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

We investigate the convergence rates of the trajectories generated by implicit first and second order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz…

Optimization and Control · Mathematics 2015-04-09 Radu Ioan Bot , Ernö Robert Csetnek

We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims…

Optimization and Control · Mathematics 2020-03-24 Radu Ioan Bot , Michael Sedlmayer , Phan Tu Vuong

In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…

Optimization and Control · Mathematics 2016-01-13 Jose Yunier Bello Cruz

The Douglas--Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one weakly and one strongly monotone operator. In this work, we…

Optimization and Control · Mathematics 2025-11-07 Jan Harold Alcantara , Akiko Takeda

We propose a Forward-Backward Truncated-Newton method (FBTN) for minimizing the sum of two convex functions, one of which smooth. Unlike other proximal Newton methods, our approach does not involve the employment of variable metrics, but is…

Optimization and Control · Mathematics 2019-11-11 Andreas Themelis , Masoud Ahookhosh , Panagiotis Patrinos

The feasibility of extrapolation of completely monotone functions can be quantified by examining the worst case scenario, whereby a pair of completely monotone functions agree on a given interval to a given relative precision, but differ as…

Complex Variables · Mathematics 2024-02-02 Henry J. Brown , Yury Grabovsky

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

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…

Optimization and Control · Mathematics 2022-11-01 A. A. Titov , S. S. Ablaev , M. S. Alkousa , F. S. Stonyakin , A. V. Gasnikov

In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…

Optimization and Control · Mathematics 2023-11-10 Emilie Chouzenoux , Jean-Christophe Pesquet , Fernando Roldán

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

Optimization and Control · Mathematics 2022-02-10 Yujia Jin , Aaron Sidford , Kevin Tian

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Optimization and Control · Mathematics 2020-05-29 Rohit Kannan , James Luedtke

We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…

Optimization and Control · Mathematics 2012-07-03 Vijay Krishnamurthy , Alexandre d'Aspremont

In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…

Optimization and Control · Mathematics 2021-09-24 Kristian Bredies , Enis Chenchene , Dirk A. Lorenz , Emanuele Naldi