Modified self-adaptive projection method for solving pseudomonotone variational inequalities (Q548374)

The authors consider the following variational inequality problem: \[ \text{Find a vector }x'\in\Omega, \text{ such that }(x- x^*)F(x^*)\geq 0,\;\forall x\in\Omega, \] where \(\Omega\) is assumed to be a nonempty closed convex subset of \(\mathbb{R}^n\); \(F\) is assumed to be a mapping from \(\mathbb{R}^n\) into itself. For this variational inequality, a self-adaptive projection method with a new search direction is proposed. The descent property of the new search direction is proved, which is useful to guarantee the convergence. Under the relatively relaxed condition that \(F\) is continuous and pseudomonotone, the global convergence of the method is proved. Computational results are presented.