Outer approximation projection methods for solving variational inequalities

doi:10.1016/j.cnsns.2026.110881

Outer approximation projection methods for solving variational inequalities

2026-10-01

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DOI：10.1016/j.cnsns.2026.110881

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In this work, we study new approximation projection methods for solving variational inequalities. One distinctive feature is that we propose two solution mappings and prove their quasi-nonexpansiveness. Using these mappings, we develop two approximation projection algorithms for solving variational inequality problems with Lipschitz continuous cost mappings, encompassing both strongly monotone and monotone cases, and establish the convergence of the resulting iterative sequences. Finally, we test the proposed methods on several explicit examples and observe that it achieves comparable, and in some cases better, practical performance than several related methods using approximation projections in the literature.

Outer approximation projection methods for solving variational inequalities

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