English
Related papers

Related papers: Non-Lipschitz Inertial Contraction-Type Method for…

200 papers

In this paper, a novel modified proximal dynamical system is proposed to compute the solution of a mixed variational inequality problem (MVIP) within a fixed time, where the time of convergence is finite and is uniformly bounded for all…

Optimization and Control · Mathematics 2022-10-21 Kunal Garg , Mayank Baranwal , Rohit Gupta , Mouhacine Benosman

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

This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…

Optimization and Control · Mathematics 2021-06-15 Pankaj Gautam , D. R. Sahu , J. C. Yao

The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…

Optimization and Control · Mathematics 2018-04-26 Dang Van Hieu

We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We…

Functional Analysis · Mathematics 2013-06-04 Radu Ioan Bot , Ernö Robert Csetnek

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in…

Optimization and Control · Mathematics 2022-07-21 Olaniyi S. Iyiola , Yekini Shehu

We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Chinedu Izuchukwu , Chibueze Christian Okeke

Extragradient method (EG) (Korpelevich, 1976) is one of the most popular methods for solving saddle point and variational inequalities problems (VIP). Despite its long history and significant attention in the optimization community, there…

Optimization and Control · Mathematics 2022-02-23 Eduard Gorbunov , Nicolas Loizou , Gauthier Gidel

We consider monotone inclusions defined on a Hilbert space where the operator is given by the sum of a maximal monotone operator $T$ and a single-valued monotone, Lipschitz continuous, and expectation-valued operator $V$. We draw motivation…

Optimization and Control · Mathematics 2022-08-11 Shisheng Cui , Uday V. Shanbhag , Mathias Staudigl , Phan Tu Vuong

In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results…

Numerical Analysis · Mathematics 2024-06-12 Antonio Leitão , Joel C. Rabelo , Dirk A. Lorenz , Maximilian Winkler

We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space $\mathcal{H}$, aiming to shed light on the acceleration phenomenon for \textit{monotone inclusion} problems, which unifies a broad class of…

Optimization and Control · Mathematics 2022-11-29 Tianyi Lin , Michael. I. Jordan

We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…

Optimization and Control · Mathematics 2023-03-22 Julia Grübel , Richard Krug , Martin Schmidt , Winnifried Wollner

In this paper, a two-step inertial Tseng extragradient method involving self-adaptive and Armijo-like step sizes is introduced for solving variational inequalities with a quasimonotone cost function in the setting of a real Hilbert space.…

Optimization and Control · Mathematics 2026-01-16 Jian-Wen Peng , Jun-Jie Luo , Abubakar Adamu

Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational…

Optimization and Control · Mathematics 2025-02-06 Roman Emelyanov , Andrey Tikhomirov , Aleksandr Beznosikov , Alexander Gasnikov

In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method…

Optimization and Control · Mathematics 2025-11-07 Liqian Qin , Yuchao Tang , Jigen Peng

We propose an abstract stochastic scheme for solving a broad range of monotone operator inclusion problems in Hilbert spaces. This framework allows for the introduction of stochasticity at several levels in monotone operator splitting…

Optimization and Control · Mathematics 2026-02-13 Patrick L. Combettes , Javier I. Madariaga

The aim of this paper is to study the weak convergence analysis of sequence of iterates generated by a three-operator splitting method of Davis and Yin incorporated with two-step inertial extrapolation for solving monotone inclusion problem…

Optimization and Control · Mathematics 2024-10-03 Olaniyi S. Iyiola , Lateef O. Jolaoso , Yekini Shehu

We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…

Optimization and Control · Mathematics 2017-05-08 Radu Ioan Bot , Ernö Robert Csetnek

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian…

Optimization and Control · Mathematics 2014-02-24 Radu Ioan Bot , Ernö Robert Csetnek

In this paper, we employ Tseng's extragradient method with the self-adaptive stepsize to solve variational inequality problems involving non-Lipschitz continuous and quasimonotone operators in real Hilbert spaces. The convergence of the…

Optimization and Control · Mathematics 2025-06-10 Meiying Wang , Hongwei Liu , Jun Yang