2020
DOI: 10.23952/jano.2.2020.2.07
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Two inertial linesearch extragradient algorithms for the bilevel split pseudomonotone variational inequality with constraints

Abstract: In this paper, two modified inertial linesearch extragradient algorithms are investigated for finding a solution of the bilevel split variational inequality problem with the fixed-point constraint of a quasi-nonexpansive mapping. Two strong convergence theorems of solutions are established without the Lipschitz continuity assumption of pseudomonotone mappings.

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Cited by 4 publications
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“…On the other hand, the projection methods are important to find the numerical solution of variational inequalities. Many authors have proposed and studied different projection methods to solve the problem of variational inequalities (see for more details [10][11][12][13][14][15][16][17][18][19][20]) and others in [21][22][23][24][25][26][27][28][29][30][31][32]. In particular, Karpelevich [10] and Antipin [33] introduced the following extragradient method:…”
Section: Introductionmentioning
confidence: 99%
“…On the other hand, the projection methods are important to find the numerical solution of variational inequalities. Many authors have proposed and studied different projection methods to solve the problem of variational inequalities (see for more details [10][11][12][13][14][15][16][17][18][19][20]) and others in [21][22][23][24][25][26][27][28][29][30][31][32]. In particular, Karpelevich [10] and Antipin [33] introduced the following extragradient method:…”
Section: Introductionmentioning
confidence: 99%