Computational modeling demonstrates convergence of a second-order dynamical system for paramonotone variational inequalities, suggesting improved algorithm efficiency for equilibrium problems.
In this paper, we propose a second-order dynamical system with a smoothing effect for solving paramonotone variational inequalities. Under standard assumptions, the trajectories generated by this dynamical system converge to a solution of the variational inequality problem. A time discretization of this dynamical system provides an iterative inertial projection-type method. An extension to equilibrium problems is developed. The results presented in this paper constitute a generalization and improvement upon existing findings in the literature. The effectiveness of the proposed algorithms is demonstrated through numerical examples, which also confirm the theoretical results.
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Hai et al. (2026) studied this question.
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