Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators

In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, we establish the weak convergence results in Hilbert spaces. Numerical examples are also present to show that faster behaviour of the proposed method.

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Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

Demonstratio Mathematica ◽

10.1515/dema-2020-0013 ◽

2020 ◽

Vol 53 (1) ◽

pp. 208-224 ◽

Cited By ~ 1

Author(s):

Timilehin Opeyemi Alakoya ◽

Lateef Olakunle Jolaoso ◽

Oluwatosin Temitope Mewomo

Keyword(s):

Variational Inequality ◽

Strong Convergence ◽

Extragradient Method ◽

Lipschitz Constant ◽

Monotone Mapping ◽

Variational Inequality Problems ◽

Step Size ◽

Lipschitz Continuous ◽

Convergence Results ◽

Monotone Variational Inequality

AbstractIn this work, we introduce two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm requires the computation of only one projection onto the feasible set per iteration while the second algorithm needs the computation of only one projection onto a half-space, and prior knowledge of the Lipschitz constant of the monotone mapping is not required in proving the strong convergence theorems for the two algorithms. Under some mild assumptions, we prove strong convergence results for the proposed algorithms to a solution of a VIP. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the proposed algorithms.

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ALGORITHM FOR VARIATIONAL INEQUALITY PROBLEM OVER THE SET OF SOLUTIONS THE EQUILIBRIUM PROBLEMS

Journal of Numerical and Applied Mathematics ◽

10.17721/2706-9699.2020.1.02 ◽

2020 ◽

pp. 18-30

Author(s):

Ya. I. Vedel ◽

S. V. Denisov ◽

V. V. Semenov

Keyword(s):

Variational Inequality ◽

Equilibrium Problems ◽

Variational Inequality Problem ◽

Proximal Method ◽

Iterative Regularization ◽

Inequality Problem ◽

Lipschitz Continuous ◽

Convergence Of Sequences ◽

Continuous Operators ◽

Monotone Bifunctions

In this paper, we consider bilevel problem: variational inequality problem over the set of solutions the equilibrium problems. To solve this problem, an iterative algorithm is proposed that combines the ideas of a two-stage proximal method and iterative regularization. For monotone bifunctions of Lipschitz type and strongly monotone Lipschitz continuous operators, the theorem on strong convergence of sequences generated by the algorithm is proved.

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New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds

Fixed Point Theory and Algorithms for Sciences and Engineering ◽

10.1186/s13663-021-00689-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Konrawut Khammahawong ◽

Poom Kumam ◽

Parin Chaipunya ◽

Somyot Plubtieng

Keyword(s):

Variational Inequality ◽

Numerical Experiments ◽

Vector Fields ◽

Variational Inequality Problem ◽

Variational Inequality Problems ◽

Hadamard Manifolds ◽

Extragradient Methods ◽

Continuous Vector ◽

Inequality Problem ◽

Lipschitz Continuous

AbstractWe propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.

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