The forward-backward algorithm and the normal problem
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Publication:6276299
DOI10.1007/S10957-017-1113-4arXiv1608.02240MaRDI QIDQ6276299
Publication date: 7 August 2016
Abstract: The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory.
Numerical mathematical programming methods (65K05) Numerical methods involving duality (49M29) Numerical optimization and variational techniques (65K10) Monotone operators and generalizations (47H05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Duality theory (optimization) (49N15) Decomposition methods (49M27) Perturbations of nonlinear operators (47H14)
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