Print Email Facebook Twitter Necessary conditions for linear convergence of iterated expansive, set-valued mappings Title Necessary conditions for linear convergence of iterated expansive, set-valued mappings Author Luke, D. Russell (University of Göttingen) Teboulle, Marc (Tel Aviv University) Nguyen, Hieu Thao (TU Delft Team Raf Van de Plas; Cantho University) Date 2018 Abstract We present necessary conditions for monotonicity of fixed point iterations of mappings that may violate the usual nonexpansive property. Notions of linear-type monotonicity of fixed point sequences—weaker than Fejér monotonicity—are shown to imply metric subregularity. This, together with the almost averaging property recently introduced by Luke et al. (Math Oper Res, 2018. https://doi.org/10.1287/moor.2017.0898), guarantees linear convergence of the sequence to a fixed point. We specialize these results to the alternating projections iteration where the metric subregularity property takes on a distinct geometric characterization of sets at points of intersection called subtransversality. Subtransversality is shown to be necessary for linear convergence of alternating projections for consistent feasibility. Subject Almost averaged mappingsAveraged operatorsCalmnessCyclic projectionsElemental regularityFeasibilityFejér monotoneFixed point iterationFixed pointsMetric regularityMetric subregularityNonconvexNonexpansiveSubtransversalityTransversality To reference this document use: http://resolver.tudelft.nl/uuid:a708f3d1-5036-406d-8150-53dbc231ea13 DOI https://doi.org/10.1007/s10107-018-1343-8 Embargo date 2019-10-26 ISSN 0025-5610 Source Mathematical Programming, 180 (2020), 1-31 Bibliographical note Accepted Author Manuscript Part of collection Institutional Repository Document type journal article Rights © 2018 D. Russell Luke, Marc Teboulle, Hieu Thao Nguyen Files PDF Necessary_conditions_for_ ... ppings.pdf 522.4 KB Close viewer /islandora/object/uuid:a708f3d1-5036-406d-8150-53dbc231ea13/datastream/OBJ/view