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Finding a zero of a sum of maximally monotone operators is a fundamentalproblem in modern optimization and nonsmooth analysis. Assuming that theresolvents of the operators are available, this problem can be tackled with theDouglas-Rachford algorithm. However, when dealing with three or more operators,one must work in a product space with as many factors as there are operators.In groundbreaking recent work by Ryu and by Malitsky and Tam, it was shown thatthe number of factors can be reduced by one. A similar reduction was achievedrecently by Campoy through a clever reformulation originally proposed byKruger. All three splitting methods guarantee weak convergence to some solutionof the underlying sum problem; strong convergence holds in the presence ofuniform monotonicity.  In this paper, we provide a case study when the operators involved are normalcone operators of subspaces and the solution set is thus the intersection ofthe subspaces. Even though these operators lack strict convexity, we show thatstriking conclusions are available in this case: strong (instead of weak)convergence and the solution obtained is (not arbitrary but) the projectiononto the intersection. Numerical experiments to illustrate our results are alsoprovided.

The splitting algorithms by Ryu, by Malitsky-Tam, and by Campoy applied  to normal cones of linear subspaces converge strongly to the projection onto  the intersection