Ryazantseva, I. P. First-order methods for certain quasi-variational inequalities in a Hilbert space. (Russian, English) Zbl 1210.39028 Zh. Vychisl. Mat. Mat. Fiz. 47, No. 2, 189-196 (2007); translation in Comput. Math. Math. Phys. 47, No. 2, 183-190, (2007). Summary: Sufficient conditions are obtained for quasi-variational inequalities of a special type with nonlinear operators in a Hilbert space to be uniquely solvable. A first-order continuous method and its discrete variant are constructed for inequalities of this kind. The strong convergence of these methods is proved. Cited in 14 Documents MSC: 39B62 Functional inequalities, including subadditivity, convexity, etc. Keywords:quasi-variational inequalities; first-order continuous method; iteration PDF BibTeX XML Cite \textit{I. P. Ryazantseva}, Zh. Vychisl. Mat. Mat. Fiz. 47, No. 2, 189--196 (2007; Zbl 1210.39028); translation in Comput. Math. Math. Phys. 47, No. 2, 183--190, (2007) Full Text: DOI OpenURL