Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems
TLDR
Two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces with strong convergence results are introduced.Abstract:
Abstract In 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.read more
Citations
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Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
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Viscosity S-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems
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A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings
Abd-semii Oluwatosin-Enitan Owolabi,Timilehin Opeyemi Alakoya,Adeolu Taiwo,Oluwatosin Temitope Mewomo +3 more
TL;DR: In this article, a modified self-adaptive inertial subgradient extragradient algorithm is presented, in which the two projections are made onto some half spaces and under mild conditions, the sequence generated by the proposed algorithm for approximating a common solution of variational inequality problem and common fixed point of a finite family of demicontractive mappings in a real Hilbert space.
Journal ArticleDOI
Viscosity S-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems
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Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces
TL;DR: In this paper, a parallel iterative scheme with viscosity approximation method was proposed, which converges strongly to a solution of the multiple-set split equality common fixed point problem for quasi-pseudocontractive mappings in real Hilbert spaces.
References
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Book
Finite-Dimensional Variational Inequalities and Complementarity Problems
TL;DR: Newton Methods for Nonsmooth Equations as mentioned in this paper and global methods for nonsmooth equations were used to solve the Complementarity problem in the context of non-complementarity problems.
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TL;DR: In this paper, the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. A One Phase Stefan Problem Bibliography Index.
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Some methods of speeding up the convergence of iteration methods
TL;DR: In this article, the authors consider the problem of minimizing the differentiable functional (x) in Hilbert space, so long as this problem reduces to the solution of the equation grad(x) = 0.