Resolvent equations technique for general variational inclusions (Q2747003)

Let \(H\) be a real Hilbert space, \(T,g:H\to H\) be two nonlinear mappings, and \(A:H\to 2^H\) be a maximal monotone mapping. The author considers the following generalized variational inclusion of finding \(u\in H\) such that \(0\in Tu+A(g(u))\). By using the resolvent operator method, he suggests some iterative algorithms for solving the generalized variational inclusion. Under the conditions that the mappings \(T\) and \(g\) are both strongly monotone and Lipschitz continuous, the author proves that the generalized variational inclusion has a solution and the sequence generated by the algorithm converges to this solution.