An LS-free splitting method for composite mappings
This paper gives a new splitting method for variational inclusion of the form \(0 \in A^TTA(x)\), where \(A\) is an \(m \times n \) matrix, \(T:R^m \rightrightarrows R^m\) is a maximal monotone mapping, and \(A^T\) denotes the transpose of \(A\). Compared with Pennanen's recently proposed method [\textit{T. Pennanen}, Numer. Funct. Anal. Optimization 23, No.~7--8, 875--890 (2002; Zbl 1054.49022)], our new scheme is free of the least squares subproblem at each iteration. Its global convergence is proven under maximal monotonicity of \(T\) and the existence of a solution.
scientific article; zbMATH DE number 5001480