New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings

DOI10.1007/s11075-020-00977-8zbMath1465.65054OpenAlexW3045374966MaRDI QIDQ2028022

Xiao-Huan Li, Simeon Reich, Duong Viet Thong, Qiao-Li Dong, Vu Tien Dung

Publication date: 31 May 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-020-00977-8

zbMATH Keywords

strong convergenceweak convergencevariational inequalitypseudomonotone operatorviscosity methodprojection-type method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical methods for variational inequalities and related problems (65K15) Numerical analysis in abstract spaces (65J99)

Related Items (18)

Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems ⋮ New Bregman projection methods for solving pseudo-monotone variational inequality problem ⋮ Strong convergence results for quasimonotone variational inequalities ⋮ On Mann implicit composite subgradient extragradient methods for general systems of variational inequalities with hierarchical variational inequality constraints ⋮ Revisiting subgradient extragradient methods for solving variational inequalities ⋮ A projection and contraction method with adaptive step sizes for solving bilevel pseudo-monotone variational inequality problems ⋮ Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem ⋮ Accelerated Bregman projection rules for pseudomonotone variational inequalities and common fixed point problems ⋮ A novel method for finding minimum-norm solutions to pseudomonotone variational inequalities ⋮ Novel projection methods for solving variational inequality problems and applications ⋮ Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces ⋮ An inertial subgradient extragradient method with Armijo type step size for pseudomonotone variational inequalities with non-Lipschitz operators in Banach spaces ⋮ Explicit extragradient-like method with adaptive stepsizes for pseudomonotone variational inequalities ⋮ On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications ⋮ Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators ⋮ Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators ⋮ Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications ⋮ Inertial method for split null point problems with pseudomonotone variational inequality problems

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