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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 paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…

Optimization and Control · Mathematics 2023-04-18 Aleksandr Beznosikov , Alexander Gasnikov , Karina Zainulina , Alexander Maslovskiy , Dmitry Pasechnyuk

We propose a linesearch projection algorithm for solving non-monotone and non-Lipschitzian equilibrium problems in Hilbert spaces. It is proved that the sequence generated by the proposed algorithm converges strongly to a solution of the…

Optimization and Control · Mathematics 2021-03-04 Lanmei Deng , Rong Hu , Yaping Fang

The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…

Optimization and Control · Mathematics 2020-01-29 Martin Burger , Elena Resmerita , Martin Benning

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

Optimization and Control · Mathematics 2020-08-31 Zheng Zhou , Bing Tan , Songxiao Li

This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…

Optimization and Control · Mathematics 2025-09-09 Watanjeet Singh , Sumit Chandok

Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…

Numerical Analysis · Mathematics 2015-06-10 Silvia Bonettini , Federica Porta , Valeria Ruggiero

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

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…

Optimization and Control · Mathematics 2018-09-18 Yekini Shehu , Phan Tu Vuong , Alain Zemkoho

We propose an inertial forward-backward splitting algorithm to compute the zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in…

Optimization and Control · Mathematics 2015-07-06 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…

Numerical Analysis · Mathematics 2018-03-06 Michael Griebel , Peter Oswald

In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…

Optimization and Control · Mathematics 2024-04-10 Hoa T. Bui , Regina S. Burachik , Evgeni A. Nurminski , Matthew K. Tam

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

This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…

Numerical Analysis · Mathematics 2019-12-18 Weimin Han , Mircea Sofonea

We study a bilevel variational inequality problem where the feasible set is itself the solution set of another variational inequality. Motivated by the difficulty of computing projections onto such sets, we consider a regularized…

Optimization and Control · Mathematics 2025-07-23 M. Marques Alves , Kangming Chen , Ellen H. Fukuda

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…

Optimization and Control · Mathematics 2009-12-23 Y. Censor , W. Chen , P. L. Combettes , R. Davidi , G. T. Herman

This study explores an inertial-based contraction-type approach for addressing monotone variational inclusion problems (in short, MVIP) within real Hilbert spaces. Most contraction-type techniques assume Lipschitz continuity and…

Optimization and Control · Mathematics 2026-04-09 Feeroz Babu , Syed Shakaib Irfan , Jen-Chih Yao , Xiaopeng Zhao

The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…

Optimization and Control · Mathematics 2018-04-26 E. E. A. Batista , G. C. Bento , O. P. Ferreira

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

Optimization and Control · Mathematics 2018-04-19 Laurentiu Leustean , Adriana Nicolae , Andrei Sipos

Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…

Optimization and Control · Mathematics 2026-02-10 Roger Behling , Yunier Bello-Cruz , Alfredo Iusem , Di Liu , Luiz-Rafael Santos