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It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…

Optimization and Control · Mathematics 2018-04-30 Le Dung Muu , Phung Minh Duc , Xuan Thanh Le

The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…

Machine Learning · Computer Science 2023-08-22 Ouail Kitouni , Niklas Nolte , Mike Williams

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…

Optimization and Control · Mathematics 2023-12-25 Luca Calatroni , Guillaume Garrigos , Lorenzo Rosasco , Silvia Villa

We show that the augmented primal-dual gradient algorithms can achieve global exponential convergence with partially strongly convex functions. In particular, the objective function only needs to be strongly convex in the subspace…

Optimization and Control · Mathematics 2025-03-12 Mengmou Li , Masaaki Nagahara

This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…

Functional Analysis · Mathematics 2014-03-14 Ibrahim Karahan , Murat Ozdemir

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

Analysis of PDEs · Mathematics 2019-11-06 Guangyu Gao , Bo Han , Shanshan Tong

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…

Optimization and Control · Mathematics 2015-07-10 Tianyi Lin , Shiqian Ma , Shuzhong Zhang

We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…

Optimization and Control · Mathematics 2015-02-23 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

In this paper, we introduce an inertial Tseng's extragradient method for solving multi-valued variational inequalits, in which only one projection is needed at each iterate. We also obtain the strong convergence results of the proposed…

Optimization and Control · Mathematics 2020-11-26 Changjie Fang , Ruirui Zhang , Shenglan Chen

The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…

Optimization and Control · Mathematics 2024-11-01 Xiao Li , Lei Zhao , Daoli Zhu , Anthony Man-Cho So

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…

Optimization and Control · Mathematics 2024-01-11 Vu Cong Bang , Dimitri Papadimitriou , Vu Xuan Nham

We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…

Numerical Analysis · Mathematics 2007-05-23 Abdenasser Benahmed

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…

Optimization and Control · Mathematics 2014-01-09 Anatoli Iouditski , Yuri Nesterov

We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…

Optimization and Control · Mathematics 2019-12-20 Sebastian Banert , Radu Ioan Bot , Ernö Robert Csetnek

In this paper we prove the strong convergence of the explicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined on Hilbert space, which solves the the variational inequality on the fixed points…

Functional Analysis · Mathematics 2011-05-03 Farrukh Mukhamedov , Mansoor Saburov

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…

Optimization and Control · Mathematics 2021-01-14 Caroline Geiersbach , Teresa Scarinci

In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…

Dynamical Systems · Mathematics 2024-06-28 Oday Hazaimah

This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…

Functional Analysis · Mathematics 2014-03-17 Ibrahim Karahan , Murat Ozdemir

We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…

Numerical Analysis · Mathematics 2018-06-05 Robert Plato , Bernd Hofmann

We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions…

Optimization and Control · Mathematics 2022-05-05 Avinash Dixit , D. R. Sahu , Pankaj Gautam , T. Som