A product space reformulation with reduced dimension for splitting algorithms
提出一种新的乘积空间重构方法，将希尔伯特空间上的多算子单调包含问题转化为等价的二算子问题，并降低乘积空间维度，从而得到变量数更少的并行分裂算法变体，收敛性无需额外假设。
Abstract In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra’s classical reformulation with a different decomposition, which results in a reduction of the dimension of the outcoming product Hilbert space. We discuss the case of not necessarily convex feasibility and best approximation problems. By applying existing splitting methods to the proposed reformulation we obtain new parallel variants of them with a reduction in the number of variables. The convergence of the new algorithms is straightforwardly derived with no further assumptions. The computational advantage is illustrated through some numerical experiments.