Algorithms for the Split Variational Inequality Problem
TL;DR: In this article, the authors propose a split variational inequality problem (SVIP), which is a SIP with the same problem-like structure as the Split Inverse Problem.
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Abstract: We propose a prototypical Split Inverse Problem (SIP) and a new variational problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse problem (e.g., a Variational Inequality Problem (VIP)), the image of which under a given bounded linear transformation is a solution of another inverse problem such as a VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.
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Citations
Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces
Rapeepan Kraikaew,Satit Saejung +1 more
TL;DR: This work proves the strong convergence of the iterative sequence generated by a modification of this method by means of the Halpern method and considers the problem of finding a common element of the solution set of a variational inequality and the fixed-point set of an quasi-nonexpansive mapping with a demiclosedness property.
250
A relaxed alternating CQ-algorithm for convex feasibility problems
TL;DR: In this article, the authors present and study the convergence of a relaxed alternating CQ-algorithm (RACQA) and show that the sequences generated by such an algorithm weakly converge to a solution.
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Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem
TL;DR: In this paper, the authors considered the split feasibility problem in infinite-dimensional Hilbert spaces, and studied the relaxed extragradient methods for finding a common element of the solution set Γ of SFP and the set Fix (S ) of fixed points of a nonexpansive mapping S.
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Modified subgradient extragradient method for variational inequality problems
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TL;DR: An algorithm as combination between the subgradient extragradient method and inertial method for solving variational inequality problems in Hilbert spaces is introduced and the weak convergence of the algorithm is established under standard assumptions imposed on cost operators.
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An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping
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TL;DR: It is proved that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping which is the unique solution of the variational inequality problem.
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