The Feasible Inexact Projected Extragradient Method for Solving Quasimonotone Variational Inequality Problems in Hilbert Space

Key words:  Variational  inequality problem, Inexact  projection, Quasimonotone  mapping, Strong  convergence

Abstract:

In this study, a new extragradient algorithm is proposed, which combines an inexact projection operator with relative error to solve quasimonotone variational inequality problems in infinite-dimensional Hilbert space. The algorithm integrates a feasible inexact projection operator into the classical extragradient framework, and theoretical analysis shows that the method has weak convergence under the assumption that the operator is Lipschitz continuous. In addition, the strong convergence of the iterative sequence is guaranteed when the operator exhibits strong pseudomonotonicity. The effectiveness and practical performance of the algorithm are demonstrated through numerical experiments on typical problem instances. The proposed approach contributes to the advancement of variational inequality theory by extending the applicability of extragradient methods to broader classes of operators. It also provides a scalable and efficient solution paradigm for large-scale optimization problems involving quasimonotone structures.