Mixed quasi variational inequalities.
The author studies the ``mixed quasi variational inequality problem'', that is, the problem of finding \(u\in H\) such that for all \(v\in H\), \[ \langle T(u),v-u\rangle+\varphi(v,u)-\varphi(u,u)\geq0, \] where \(H\) is a Hilbert space, \(T:H\rightarrow H\) is a non-linear operator and \(\varphi:H\times H\rightarrow\mathbb{R}\cup\{+\infty\}\) is a continuous bifunction. This is a part of a long series of papers of the author, studying iterative algorithms via the ``auxiliary principle technique'' under a standard generalized monotonicity assumption on the operator \(T\). In the last part, the paper discusses links with projected dynamical systems.
scientific article; zbMATH DE number 2009056