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• W4229070703 abstract "Abstract In this paper, we introduce two subgradient extragradient-type algorithms for solving variational inequality problems in the real Hilbert space. The first one can be applied when the mapping f is strongly pseudomonotone (not monotone) and Lipschitz continuous. The first algorithm only needs two projections, where the first projection onto closed convex set C and the second projection onto a half-space $C_{k}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:math> . The strong convergence theorem is also established. The second algorithm is relaxed and self-adaptive; that is, at each iteration, calculating two projections onto some half-spaces and the step size can be selected in some adaptive ways. Under the assumption that f is monotone and Lipschitz continuous, a weak convergence theorem is provided. Finally, we provide numerical experiments to show the efficiency and advantage of the proposed algorithms." @default.
• W4229070703 created "2022-05-08" @default.
• W4229070703 creator A5030244952 @default.
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• W4229070703 date "2022-05-07" @default.
• W4229070703 modified "2023-09-25" @default.
• W4229070703 title "Self-adaptive subgradient extragradient-type methods for solving variational inequalities" @default.
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• W4229070703 doi "https://doi.org/10.1186/s13660-022-02793-1" @default.
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