Abstract
In this paper, we continue to investigate the convergence analysis of Tseng-type forward-backward-forward algorithms for solving quasimonotone variational inequalities in Hilbert spaces. We use a self-adaptive technique to update the step sizes without prior knowledge of the Lipschitz constant of quasimonotone operators. Furthermore, we weaken the sequential weak continuity of quasimonotone operators to a weaker condition. Under some mild assumptions, we prove that Tseng-type forward-backward-forward algorithm converges weakly to a solution of quasimonotone variational inequalities.
Highlights
Let H be a real Hilbert space endowed with inner product h·, · i and corresponding norm ∥·∥
Our purpose of this paper is to investigate the following Stampacchia-type variational inequality
0: ð3Þ Journal of Function Spaces. This algorithm guarantees the convergence of the sequence fukg defined by (3) if f is pseudomonotone
Summary
Let H be a real Hilbert space endowed with inner product h·, · i and corresponding norm ∥·∥. This algorithm guarantees the convergence of the sequence fukg defined by (3) if f is pseudomonotone. Bot et al ([48]) proved that the sequence fukg generated by (6) converges weakly to an element in SolðC, f Þ provided f is pseudomonotone and sequentially weakly continuous. We show that the proposed algorithm converges weakly to a solution of quasimonotone variational inequalities under some additional conditions.
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