Pseudomonotone Variational Inequalities Research Articles

A new projection and contraction method for solving split monotone variational inclusion, pseudomonotone variational inequality, and common fixed point problems

A new projection and contraction method for solving split monotone variational inclusion, pseudomonotone variational inequality, and common fixed point problems

A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities

A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities

Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem

In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.

A Relaxed Inertial Factor of the Modified Subgradient Extragradient Method for Solving Pseudo Monotone Variational Inequalities in Hilbert Spaces

A Relaxed Inertial Factor of the Modified Subgradient Extragradient Method for Solving Pseudo Monotone Variational Inequalities in Hilbert Spaces

A novel accelerated extragradient algorithm to solve pseudomonotone variational inequalities

In this paper, we propose a new inertial iterative method to solve classical variational inequalities with pseudomonotone and Lipschitz continuous operators in the setting of a real Hilbert space. The proposed iterative scheme is basically analogous to the extragradient method used to solve the problems of variational inequalities in real Hilbert spaces. The strong convergence of the proposed algorithm is set up with the prior knowledge of Lipschitz’s constant of an operator. Finally, several computational experiments are listed to show the applicability and efficiency of the proposed algorithm.

An extragradient inertial algorithm for solving split fixed-point problems of demicontractive mappings, with equilibrium and variational inequality problems

Abstract The purpose of this article is to study and analyse a new extragradient-type algorithm with an inertial extrapolation step for solving split fixed-point problems for demicontractive mapping, equilibrium problem, and pseudomonotone variational inequality problem in real Hilbert spaces. One of the advantages of the proposed algorithm is that a strong convergence result is achieved without a prior estimate of the Lipschitz constant of the cost operator, which is very difficult to find. In addition, the stepsize is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the cost operator. Some numerical experiments are reported to show the performance and behaviour of the sequence generated by our algorithm. The obtained results in this article extend and improve many related recent results in this direction in the literature.

Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces

Abstract The projection technique is a very important method and efficient for solving variational inequality problems. In this study, we developed the subgradient extragradient method for solving pseudomonotone variational inequality in real Hilbert spaces. Our first algorithm requires only computing one projection onto the feasible set per iteration and the strong convergence is proved without the prior knowledge of the Lipschitz constant as well as the sequentially weak continuity of the associated mapping. The second algorithm uses the linesearch procedure such that its convergence does not require the Lipschitz continuous condition of the variational inequality mapping. Finally, some numerical experiments are provided to demonstrate the advantages and efficiency of the proposed methods.

Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications

We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.

An improved algorithm with Armijo line-search rule for solving pseudomonotone variational inequality problems in Banach spaces

An improved algorithm with Armijo line-search rule for solving pseudomonotone variational inequality problems in Banach spaces

Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces

Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces

Inertial projection methods for finding a minimum-norm solution of pseudomonotone variational inequality and fixed-point problems

Inertial projection methods for finding a minimum-norm solution of pseudomonotone variational inequality and fixed-point problems

Fixed-time stability of projection neurodynamic network for solving pseudomonotone variational inequalities

In this paper, we propose a novel modified neurodynamic network (MNN) based on projection to solve pseudomonotone variational inequalities. Under the strong pseudo-monotonicity and Lipschitz continuous assumptions, the MNN admits a unique solution. The relations between the MNN and the corresponding neurodynamic network are obtained. Moreover, we establish the globally fixed-time stability of the MNN. The convergence time of the MNN is not depended on the initial conditions and uniformly bounded. Numerical examples are also reported to show the effectiveness and superiority of the MNN.

A self-adaptive stochastic subgradient extragradient algorithm for the stochastic pseudomonotone variational inequality problem with application

A self-adaptive stochastic subgradient extragradient algorithm for the stochastic pseudomonotone variational inequality problem with application

A new modified extragradient method with line-search process for solving pseudomonotone variational inequality in Hilbert spaces

ABSTRACT In this paper, we mainly introduce a new algorithm with a different line-search process for solving variational inequality problem of pseudomonotone and non-Lipschitz operators in real Hilbert spaces. Under some appropriate restrictions imposed on the parameters, we prove a strong convergence theorem for finding an element of solutions of variational inequality problem. At the same time, we give some numerical examples to illustrate the effectiveness of our proposed algorithm. The main results obtained in this paper extend and improve many recent ones in the literature.

A New Projection-type Method with Nondecreasing Adaptive Step-sizes for Pseudo-monotone Variational Inequalities

A New Projection-type Method with Nondecreasing Adaptive Step-sizes for Pseudo-monotone Variational Inequalities

Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks

A novel class of implicit constitutive relations is studied, wherein the stress and the linearized strain appear linearly, that describe material response in elastic porous bodies like rocks, ceramics, concrete, cement, bones and metals. The constitutive relation is applied to a body with a crack subjected to non-penetration conditions between the opposite crack faces. To treat well-posedness of a corresponding variational inequality, we rely on a new approximation by thresholding dilatation and apply the Lions existence theorem on pseudo-monotone variational inequalities. An analytical solution to a specific example (without crack) under uniform triaxial loading is constructed, wherein blow-up can take place at a finite load, and this difficulty is overcome within a thresholding approximation so that blow-up does not occur.

Fast alternated inertial projection algorithms for pseudo-monotone variational inequalities

In this paper, we propose an alternated inertial subgradient extragradient algorithm for variational inequalities with self-adaptive step-sizes and obtain weak and linear convergence results. We also obtain linear convergence results using an alternated inertial projected gradient algorithm for which knowledge of the modulus of strong pseudo-monotonicity and Lipschitz constant of the cost function are not needed. We compare numerically our algorithms with other projection-type algorithms in the literature.

An inertial subgradient-extragradient algorithm for solving pseudomonotone variational inequalities

An inertial subgradient-extragradient algorithm for solving pseudomonotone variational inequalities

Revisiting the extragradient method for finding the minimum-norm solution of non-Lipschitzian pseudo-monotone variational inequalities

Revisiting the extragradient method for finding the minimum-norm solution of non-Lipschitzian pseudo-monotone variational inequalities

An inertia-based algorithm for pseudomonotone variational inequality and fixed point problems in real Hilbert space

The aim of this work is to study a pseudomonotone variational inequality and a fixed point problem involving pseudocontractive mappings in real Hilbert spaces. We introduce an inertia-based iterative algorithm for finding a common solution to this problem. The strong convergence of the proposed algorithm is proved. Finally, numerical examples are provided and also meaningful comparisons of these results with those in [Y. Yao, M. Postolache, J. C. Yao, Mathematics, \(\textbf{7}\) (2019), 14 pages], proving that at our proposed numerical schemes are more efficient.