Projective splitting methods for sums of maximal monotone operators with applications

Splitting methods for sums of maximal monotone operators are studied in this paper. By formulating the classical splitting methods, including the Douglas/Peaceman–Rachford splitting and the forward–backward splitting, into fixed point iterations, general splitting methods are considered via parameterizing fixed point formulas. Weak convergence results for these general splitting methods are derived with the help of a demiclosedness principle. Moreover, by employing the Haugazeau-like projective method, the weak convergence splitting algorithms are forced to be strongly convergent. Finally, applications to the convex feasibility and best approximation problems are made from the viewpoint of convex optimization; new and improved convergence results for solving these two problems are obtained.