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We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

Optimization and Control · Mathematics 2024-02-14 Alberto De Marchi

In infinite-dimensional Hilbert spaces we device a class of strongly convergent primal-dual schemes for solving variational inequalities defined by a Lipschitz continuous and pseudomonote map. Our novel numerical scheme is based on Tseng's…

Optimization and Control · Mathematics 2019-08-27 Benoit Duvocelle , Dennis Meier , Mathias Staudigl , Phan Tu Vuong

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

This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…

Functional Analysis · Mathematics 2025-12-16 M. H. M. Rashid

We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…

Optimization and Control · Mathematics 2024-10-07 Aleksandr Beznosikov , Darina Dvinskikh , Dmitry Bylinkin , Andrei Semenov , Alexander Gasnikov

In this paper, we consider the monotone generalized variational inequality (MGVI) where the monotone operator is Lipschitz continuous. Inspired by the extragradient method and the projection contraction algorithms for monotone variational…

Optimization and Control · Mathematics 2020-09-09 Yu You

We propose a variable metric extension of the forward--backward-forward algorithm for finding a zero of the sum of a maximally monotone operator and a Lipschitzian monotone operator in Hilbert spaces. In turn, this framework provides a…

Optimization and Control · Mathematics 2012-11-01 B. C. Vũ

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give…

Optimization and Control · Mathematics 2021-01-21 Yekini Shehu , Olaniyi. S. Iyiola

We introduce an inexact oracle model for variational inequalities (VI) with monotone operator, propose a numerical method which solves such VI's and analyze its convergence rate. As a particular case, we consider VI's with…

Optimization and Control · Mathematics 2022-02-18 Fedor Stonyakin , Alexander Gasnikov , Pavel Dvurechensky , Mohammad Alkousa , Alexander Titov

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

Optimization and Control · Mathematics 2021-02-18 Nguyen Van Dung , Bang Cong Vu

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 general extra-gradient scheme for solving monotone variational inequalities (VI), referred to here as Approximation-based Regularized Extra-gradient method (ARE). The first step of ARE solves a VI subproblem with…

Optimization and Control · Mathematics 2022-10-11 Kevin Huang , Shuzhong Zhang

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

Optimization and Control · Mathematics 2011-01-10 Luis M. Briceño-Arias

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

Optimization and Control · Mathematics 2018-03-26 Yu. Malitsky

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

In this paper, under the monotonicity of pairs of operators, we propose some Generalized Proximal Point Algorithms to solve non-monotone inclusions using warped resolvents and transformed resolvents. The weak, strong, and linear convergence…

Optimization and Control · Mathematics 2025-01-24 Ba Khiet Le , Minh N. Dao , Michel Théra

We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under…

Optimization and Control · Mathematics 2018-09-12 Minh N. Dao , Hung M. Phan

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…

Optimization and Control · Mathematics 2017-11-29 Regina S. Burachik , R. Díaz Millán

In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing…

Optimization and Control · Mathematics 2013-11-13 Cong D. Dang , Guanghui Lan

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…

Numerical Analysis · Mathematics 2020-12-25 Leon Bungert , Martin Burger , Yury Korolev , Carola-Bibiane Schoenlieb