Abstract
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility problems defined by finitely many sets, some other require the use of a product space reformulation to construct equivalent problems with two sets. In this work we analyze how some regularity properties are preserved under a reformulation in a product space of reduced dimension. This allows us to establish local linear convergence of parallel projection methods which are constructed through this reformulation.
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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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The author would like to thank two anonymous referees for their careful reading and their constructive comments which helped to improve this manuscript.
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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The author was partially supported by the Ministry of Science and Innovation of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PID2022-136399NB-C21, and by the Generalitat Valenciana (AICO/2021/165).
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Campoy, R. Regularity of Sets Under a Reformulation in a Product Space with Reduced Dimension. Set-Valued Var. Anal 31, 40 (2023). https://doi.org/10.1007/s11228-023-00702-2
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DOI: https://doi.org/10.1007/s11228-023-00702-2
Keywords
- Regularity
- Product space reformulation
- Feasibility problem
- Projection methods
- Nonconvex
- Super-regular set
- Linear convergence