An LS-free splitting method for composite mappings Original Research Article

This paper gives a new splitting method for variational inclusion of the form 0∈ATTA(x)0∈ATTA(x), where AA is an m×nm×n matrix, T:Rm⇉RmT:Rm⇉Rm is a maximal monotone mapping, and ATAT denotes the transpose of AA. 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 TT and the existence of a solution.