The paper extends FBF dynamics and a Bregman golden-ratio algorithm to quasimonotone variational inequalities, claiming strong convergence under only uniform continuity, but the proofs require extra assumptions not in the abstract.
Convergence Analysis of the Self-Adaptive Projection Method for Variational Inequalities with Non-Lipschitz Continuous Operators
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abstract
In this paper, we employ Tseng's extragradient method with the self-adaptive stepsize to solve variational inequality problems involving non-Lipschitz continuous and quasimonotone operators in real Hilbert spaces. The convergence of the proposed method is analyzed under some mild assumptions. The key advantages of the method are that it does not require the operator associated with the variational inequality to be Lipschitz continuous and that it adopts the self-adaptive stepsize. Numerical experiments are also provided to illustrate the effectiveness and superiority of the method.
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2025 1verdicts
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Asymptotic Properties of a Forward-Backward-Forward Differential Equation and Its Discrete Version for Solving Quasimonotone Variational Inequalities
The paper extends FBF dynamics and a Bregman golden-ratio algorithm to quasimonotone variational inequalities, claiming strong convergence under only uniform continuity, but the proofs require extra assumptions not in the abstract.