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In this paper we propose a product space reformulation to transform monotoneinclusions described by finitely many operators on a Hilbert space intoequivalent two-operator problems. Our approach relies on Pierra's classicalreformulation with a different decomposition, which results on a reduction ofthe dimension of the outcoming product Hilbert space. We discuss the case ofnot necessarily convex feasibility and best approximation problems. By applyingexisting splitting methods to the proposed reformulation we obtain new parallelvariants of them with a reduction in the number of variables. The convergenceof the new algorithms is straightforwardly derived with no further assumptions.The computational advantage is illustrated through some numerical experiments.

A Product Space Reformulation with Reduced Dimension for Splitting Algorithms