Abstract
The existence and the convergence (up to a subsequence) of the Moreau-Yosida regularization for the state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets are established. Then, by a reparametrization technique, the existence of solutions for bounded variation continuous state-dependent sweeping processes with nonregular (subsmooth and positively alpha-far) sets is proved. An application to vector hysteresis is discussed, where it is shown that the Play operator with positively alpha-far sets is well defined for bounded variation continuous inputs.
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Acknowledgements
The authors wish to thank the referees for providing several helpful suggestions. The research of the second author was supported by CONICYT-PCHA/Doctorado Nacional/2013-21130676.
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Jourani, A., Vilches, E. Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets. J Optim Theory Appl 173, 91–116 (2017). https://doi.org/10.1007/s10957-017-1083-6
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DOI: https://doi.org/10.1007/s10957-017-1083-6
Keywords
- Moreau-Yosida regularization
- Subsmooth sets
- Sweeping process
- Positively \(\alpha \)-far sets
- Measure differential inclusions
- Play operator