A Product Space Reformulation with Reduced Dimension for Splitting Algorithms
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Publication:6373793
DOI10.1007/S10589-022-00395-7arXiv2107.12355MaRDI QIDQ6373793
Publication date: 26 July 2021
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 on 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.
Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Decomposition methods (49M27)
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