An LS-free splitting method for composite mappings

This paper gives a new splitting method for variational inclusion of the form 0∈ATTA(x), where A is an m×n matrix, T:Rm⇉Rm is a maximal monotone mapping, and AT denotes the transpose of A. Compared with Pennanen's recently proposed method, 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.