Quasimonotone Variational Inequalities Research Articles

Three novel inertial subgradient extragradient methods for quasi-monotone variational inequalities in Banach spaces

Three novel inertial subgradient extragradient methods for quasi-monotone variational inequalities in Banach spaces

Viscosity extragradient algorithms with double inertial extrapolation steps for quasimonotone variational inequalities and fixed point problems

We study two viscosity extragradient algorithms with double inertial extrapolation steps for finding a common solution of a variational inequality governed by a quasimonotone operator and of a fixed point problem with a demicontractive mapping in a real Hilbert space. The strong convergence theorems are proved under certain appropriate conditions. The step sizes of our algorithms are updated by simple calculations without knowing the prior information of the operator norms. Numerical examples in finite- and infinite-dimensional spaces are given to show the performance of the proposed algorithms.

Convergence of two-step inertial Tseng’s extragradient methods for quasimonotone variational inequality problems

This paper introduces two-step inertial Tseng’s extragradient methods with self-adaptive step sizes for solving quasimonotone variational inequalities in real Hilbert spaces. Under suitable conditions on the iterative parameters, weak convergence of the sequence generated by the proposed algorithms is obtained. Numerical results demonstrate the efficiency of the methods compared to others available ones in literature.

A modified subgradient extragradient method with non-monotonic step sizes for solving quasimonotone variational inequalities

A modified subgradient extragradient method with non-monotonic step sizes for solving quasimonotone variational inequalities

A reconsideration on convergence of the extra-gradient method for solving quasimonotone variational inequalities

ABSTRACT In this paper, we continue to investigate convergence of the extra-gradient method for solving quasimonotone variational inequalities in Hilbert spaces. Under some suitable conditions, we prove that the iterative sequence generated by the extra-gradient method converges weakly to a solution of quasimonotone variational inequalities. Our result corrects and improves the main result in Salahuddin [The extra-gradient method for quasimonotone variational inequalities. Optimization. 2022;71:2519–2528].

Two-step inertial Tseng’s extragradient method for solving quasimonotone variational inequalities

We focus on quasimonotone variational inequality problems with non-Lipschitz operator and combine some operator theory techniques to establish a weak convergent fixed point iterative method to approximate the solution of the presented problems. The convergence analysis assumes very mild conditions and strictly weaker assumption on the cost operator associated with the problems and thus generalizes and extend recent related results in the literature. Finally, several numerical examples illustrate the potential and advantages of the proposed algorithm over some existing methods are presented.

Projection and contraction method with double inertial steps for quasi-monotone variational inequalities

In this paper, we present a modified projection and contraction method for solving quasi-monotone variational inequalities in real Hilbert spaces. Our proposed method is a combination of double inertial extrapolation steps, the subgradient extragradient method and the projection contraction method, which can effectively accelerate the convergence rate. The weak and linear convergence have been obtained under some suitable conditions. Some numerical experiments are given to show that our proposed method outperforms the related methods.

Strong convergent algorithm for finding minimum-norm solutions of quasimonotone variational inequalities with fixed point constraint and application

The class of quasimonotone mappings are known to be more general and applicable than the classes of pseudomonotone and monotone mappings. However, only very few results can be found in the literature on quasimonotone variational inequality problems and most of these results are on weak convergent algorithms. In this paper, we study the quasimonotone variational inequality problem (VIP) with constraint of fixed point problem (FPP) of quasi-pseudocontractive mappings. We introduce a new inertial Tseng’s extragradient method with self-adaptive step size for approximating the minimum-norm solutions of the aforementioned problem in the framework of Hilbert spaces. We prove that the sequence generated by the proposed method converges strongly to a common (minimum-norm) solution of the quasimonotone VIP and FPP of quasi-pseudocontractive mappings without the knowledge of the Lipschitz constant of the cost operator. We provide several numerical experiments for the proposed method in comparison with existing methods in the literature. Finally, we applied our result to image restoration problem. Our result improves, extends and generalizes several of the recently announced results in this direction.

On fixed point iterative methods for solving non-Lipschitz quasi-monotone variational inequalities

On fixed point iterative methods for solving non-Lipschitz quasi-monotone variational inequalities

An inertial hybrid extragradient-viscosity method for solving quasimonotone variational inequalities

An inertial hybrid extragradient-viscosity method for solving quasimonotone variational inequalities

A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities

Abstract The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.

Extragradient type projection algorithm for solving quasimonotone variational inequalities

In this paper, we propose an extragradient type projection algorithm for solving quasimonotone variational inequalities in R n . Under the assumption that f is a quasimonotone and continuous mapping and the solution set of the dual variational inequality problem is nonempty, the globally convergence of the algorithm is established. Numerical experiments are also reported.

Modified accelerated Bregman projection methods for solving quasi-monotone variational inequalities

In this paper, we introduce three new inertial-like Bregman projection methods with a nonmonotone adaptive step-size for solving quasi-monotone variational inequalities in real Hilbert spaces. Under some suitable conditions, the weak convergence of these methods is proved without the prior knowledge of the Lipschitz constant of the operator and the strong convergence of some proposed methods under a strong quasi-monotonicity assumption of the mapping is also provided. Finally, several numerical experiments and applications in image restoration problems are provided to illustrate the performance of the proposed methods.

Subgradient extragradient method with double inertial steps for quasi-monotone variational inequalities

In this paper, we present a modified subgradient extragradient method with double inertial extrapolation terms and a non-monotonic adaptive step size for solving quasi-monotone and Lipschitz continuous variational inequalities in real Hilbert spaces. Under some suitable conditions, we obtain the weak convergence theorem of our proposed algorithm. Moreover, strong convergence is obtained when the cost operator is strongly pseudo-monotone and Lipschitz continuous. Finally, several numerical results illustrate the effectiveness and competitiveness of our algorithm.

Strong convergent inertial Tseng’s extragradient method for solving non-Lipschitz quasimonotone variational inequalities in Banach spaces

Strong convergent inertial Tseng’s extragradient method for solving non-Lipschitz quasimonotone variational inequalities in Banach spaces

Strong convergence analysis for solving quasi-monotone variational inequalities and fixed point problems in reflexive Banach spaces

Strong convergence analysis for solving quasi-monotone variational inequalities and fixed point problems in reflexive Banach spaces

Strong convergence analysis of modified Mann-type forward–backward scheme for solving quasimonotone variational inequalities

The paper proposes multiple new extragradient methods for solving a variational inequality problem involving quasimonotone operators in infinite-dimensional real Hilbert spaces. These methods contain variable stepsize rules that are revised at each iteration and are dependent on prior iterations. These algorithms have the benefit of not requiring prior knowledge of the Lipschitz constant or any line-search approach. Simple conditions are used to demonstrate the algorithm’s convergence. A collection of simple experiments is presented to show the numerical behavior of the algorithms.

Strong convergence results for quasimonotone variational inequalities

Strong convergence results for quasimonotone variational inequalities

A Self-Adaptive Extragradient Algorithm for Solving Quasimonotone Variational Inequalities

This article aims to research iterative schemes for searching a solution of a quasimonotone variational inequality in a Hilbert space. For solving this quasimonotone variational inequality, we propose an iterative procedure which combines a self-adaptive rule and the extragradient algorithm. We demonstrate that the procedure weakly converges to the solution of the investigated quasimonotone variational inequality provided the considered operator satisfies several additional conditions.

A projection-like method for quasimonotone variational inequalities without Lipschitz continuity

A projection-like method for quasimonotone variational inequalities without Lipschitz continuity