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Items from 1 to 20 out of 132 results

article

Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications

Nuttapol Pakkaranang, Habib ur Rehman, Wiyada Kumam

Demonstratio Mathematica > 2021 > Vol. 54, nr 1 > 280--298

The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The...

article

A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

C. E. Chidume, M. O. Nnakwe, A. Adamu

Fixed Point Theory and Applications > 2019 > 2019 > 1 > 1-19

Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem,...

article

Accelerated Subgradient Extragradient Methods for Variational Inequality Problems

Duong Viet Thong, Nguyen The Vinh, Yeol Je Cho

Journal of Scientific Computing > 2019 > 80 > 3 > 1438-1462

In this paper, we introduce two new iterative algorithms for solving monotone variational inequality problems in real Hilbert spaces, which are based on the inertial subgradient extragradient algorithm, the viscosity approximation method and the Mann type method, and prove some strong convergence theorems for the proposed algorithms under suitable conditions. The main results in this paper improve...

article

Strong convergence of extragradient methods with a new step size for solving variational inequality problems

Duong Viet Thong, Dang Hieu

Computational and Applied Mathematics > 2019 > 38 > 3 > 1-21

In this paper, we propose two different kinds of extragradient methods with a new step size for finding an element of the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous operator in real Hilbert spaces. We only use one projection to design the algorithms and the strong convergence theorems proved without the prior knowledge of the Lipschitz constant of...

article

The viscosity method for the implicit double midpoint rule with numerical results and its applications

Shrijana Dhakal, Wutiphol Sintunavarat

Computational and Applied Mathematics > 2019 > 38 > 2 > 1-18

In this work, we present the viscosity method for the implicit double midpoint rule for finding the fixed points of nonexpansive mappings in real Hilbert spaces. The strong convergence theorem of this method is proved under some specific assumption imposed on the control parameters. Also, we present some numerical results which are presented to illustrate the proposed method and convergence results...

article

Self-adaptive subgradient extragradient method with inertial modification for solving monotone variational inequality problems and quasi-nonexpansive fixed point problems

Ming Tian, Mengying Tong

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-19

In this paper, we introduce a new algorithm with self-adaptive method for finding a solution of the variational inequality problem involving monotone operator and the fixed point problem of a quasi-nonexpansive mapping with a demiclosedness property in a real Hilbert space. The algorithm is based on the subgradient extragradient method and inertial method. At the same time, it can be considered as...

article

Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces

Duong Viet Thong, Aviv Gibali

Japan Journal of Industrial and Applied Mathematics > 2019 > 36 > 1 > 299-321

In this paper we are focused on solving monotone and Lipschitz continuous variational inequalities in real Hilbert spaces. Motivated by several recent results related to the subgradient extragradient method (SEM), we propose two SEM extensions which do not require the knowledge of the Lipschitz constant associated with the variational inequality operator. Under mild and standard conditions, we establish...

article

Some extragradient-viscosity algorithms for solving variational inequality problems and fixed point problems

Duong Viet Thong, Dang Hieu

Numerical Algorithms > 2019 > 82 > 3 > 761-789

The purpose of this paper is to study and analyze two different kinds of extragradient-viscosity-type iterative methods for finding a common element of the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous operator and the set of fixed points of a demicontractive mapping in real Hilbert spaces. Although the problem can be translated to a common fixed point...

article

Modified Tseng’s extragradient algorithms for variational inequality problems

Duong Viet Thong, Dang Hieu

Journal of Fixed Point Theory and Applications > 2018 > 20 > 4 > 1-18

In this work, our interest is in investigating the monotone variational inequality problems in the framework of real Hilbert spaces. For solving this problem, we introduce two modified Tseng’s extragradient methods using the inertial technique. The weak convergence theorems are established under the standard assumptions imposed on cost operators. Finally, numerical results are reported to illustrate...

article

New extragradient methods for solving variational inequality problems and fixed point problems

Duong Viet Thong, Dang Hieu

Journal of Fixed Point Theory and Applications > 2018 > 20 > 3 > 1-20

In this paper, we introduce two new iterative algorithms for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of solutions of the variational inequality problem with a monotone and Lipschitz continuous mapping in real Hilbert spaces, by combining a modified Tseng’s extragradient scheme with the Mann approximation method. We prove weak and strong convergence...

article

The split common fixed point problem for infinite families of demicontractive mappings

Adisak Hanjing, Suthep Suantai

Fixed Point Theory and Applications > 2018 > 2018 > 1 > 1-21

In this paper, we propose a new algorithm for solving the split common fixed point problem for infinite families of demicontractive mappings. Strong convergence of the proposed method is established under suitable control conditions. We apply our main results to study the split common null point problem, the split variational inequality problem, and the split equilibrium problem in the framework of...

article

The modified split generalized equilibrium problem for quasi-nonexpansive mappings and applications

Kanyarat Cheawchan, Atid Kangtunyakarn

Journal of Inequalities and Applications > 2018 > 2018 > 1 > 1-28

In this paper, we introduce a new problem, the modified split generalized equilibrium problem, which extends the generalized equilibrium problem, the split equilibrium problem and the split variational inequality problem. We introduce a new method of an iterative scheme {xn} $\{x_{n}\}$ for finding a common element of the set of solutions of variational inequality problems and the set of common fixed...

article

Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems

Duong Viet Thong, Dang Van Hieu

Numerical Algorithms > 2019 > 80 > 4 > 1283-1307

In this paper, basing on the subgradient extragradient method and inertial method with line-search process, we introduce two new algorithms for finding a common element of the solution set of a variational inequality and the fixed point set of a quasi-nonexpansive mapping with a demiclosedness property. The weak convergence of the algorithms are established under standard assumptions imposed on cost...

article

Weakly homogeneous variational inequalities and solvability of nonlinear equations over cones

M. Seetharama Gowda, David Sossa

Mathematical Programming > 2019 > 177 > 1-2 > 149-171

Given a closed convex cone C in a finite dimensional real Hilbert space H, a weakly homogeneous map $$f\,{:}\,C\rightarrow H$$ f : C → H is a sum of two continuous maps h and g, where h is positively homogeneous of degree $$\gamma $$ γ ( $$\ge 0$$ ≥ 0 ) on C and $$g(x)=o(||x||^\gamma )$$ g ( x ) = o ( | | x | | γ ) as $$||x||\rightarrow \infty $$ | | x | | → ∞...

article

A Modified Iterative Method for a Finite Collection of Non-self Mappings and a Family of Variational Inequality Problems

Prashanta Majee, Chandal Nahak

Mediterranean Journal of Mathematics > 2018 > 15 > 2 > 1-18

This paper deals with an iterative algorithm with the help of averaged mappings for the common solution of a fixed point problem of a finite collection of k-strictly pseudocontractive non-self mappings and a system of variational inequality problems in the setting of a real Hilbert space. Under some suitable conditions, the sequence generated by the proposed algorithm converges strongly to the common...

article

A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces

Gang Cai, Aviv Gibali, Olaniyi S. Iyiola, Yekini Shehu

Journal of Optimization Theory and Applications > 2018 > 178 > 1 > 219-239

In this paper, we study the variational inequalities involving monotone and Lipschitz continuous mapping in Banach spaces. A new and simple iterative method, which combines Halpern’s technique and the subgradient extragradient idea, is given. Under mild and standard assumptions, we establish the strong convergence of our algorithm in a uniformly smooth and convex Banach spaces. We also present a modification...

article

A new algorithm for variational inequality problems with a generalized phi-strongly monotone map over the set of common fixed points of a finite family of quasi-phi-nonexpansive maps, with applications

C. E. Chidume, U. V. Nnyaba, O. M. Romanus

Journal of Fixed Point Theory and Applications > 2018 > 20 > 1 > 1-15

Let E be a uniformly convex and uniformly smooth real Banach space with dual space $$E^*$$ E∗ and C be a nonempty, closed and convex subset of E. Let $$A:E\rightarrow E^*$$ A:E→E∗ be a generalized $$\Phi $$ Φ -strongly monotone and bounded map and let $$T_i:C\rightarrow E, i=1,2,3,\ldots , N$$ Ti:C→E,i=1,2,3,…,N be a finite family of quasi-$$\phi $$ ϕ -nonexpansive maps such that $$\cap _{i=1}^{N}...

article

Modified subgradient extragradient method for variational inequality problems

Duong Viet Thong, Dang Hieu

Numerical Algorithms > 2018 > 79 > 2 > 597-610

In this paper, we introduce an algorithm as combination between the subgradient extragradient method and inertial method for solving variational inequality problems in Hilbert spaces. The weak convergence of the algorithm is established under standard assumptions imposed on cost operators. The proposed algorithm can be considered as an improvement of the previously known inertial extragradient method...

article

Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

Mohammad Farid, Syed Shakaib Irfan, Mohammad Firdosh Khan, Suhel Ahmad Khan

Journal of Inequalities and Applications > 2017 > 2017 > 1 > 1-19

In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally,...

article

The projection and contraction methods for finding common solutions to variational inequality problems

Qiao-Li Dong, Yeol Je Cho, Themistocles M. Rassias

Optimization Letters > 2018 > 12 > 8 > 1871-1896

In this paper, we firstly introduce two projection and contraction methods for finding common solutions to variational inequality problems involving monotone and Lipschitz continuous operators in Hilbert spaces. Then, by modifying the two methods, we propose two hybrid projection and contraction methods. Both weak and strong convergence are investigated under standard assumptions imposed on the operators...

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Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications

A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

Accelerated Subgradient Extragradient Methods for Variational Inequality Problems

Strong convergence of extragradient methods with a new step size for solving variational inequality problems

The viscosity method for the implicit double midpoint rule with numerical results and its applications

Self-adaptive subgradient extragradient method with inertial modification for solving monotone variational inequality problems and quasi-nonexpansive fixed point problems

Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces

Some extragradient-viscosity algorithms for solving variational inequality problems and fixed point problems

Modified Tseng’s extragradient algorithms for variational inequality problems

New extragradient methods for solving variational inequality problems and fixed point problems

The split common fixed point problem for infinite families of demicontractive mappings

The modified split generalized equilibrium problem for quasi-nonexpansive mappings and applications

Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems

Weakly homogeneous variational inequalities and solvability of nonlinear equations over cones

A Modified Iterative Method for a Finite Collection of Non-self Mappings and a Family of Variational Inequality Problems

A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces

A new algorithm for variational inequality problems with a generalized phi-strongly monotone map over the set of common fixed points of a finite family of quasi-phi-nonexpansive maps, with applications

Modified subgradient extragradient method for variational inequality problems

Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

The projection and contraction methods for finding common solutions to variational inequality problems

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