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Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets

Author

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  • Abderrahim Jourani

    (Université de Bourgogne Franche-Comté)

  • Emilio Vilches

    (Universidad de Chile)

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.

Suggested Citation

  • Abderrahim Jourani & Emilio Vilches, 2017. "Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 91-116, April.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:1:d:10.1007_s10957-017-1083-6
    DOI: 10.1007/s10957-017-1083-6
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    References listed on IDEAS

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    1. Messaoud Bounkhel, 2012. "Regularity Concepts in Nonsmooth Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4614-1019-5, June.
    2. Tahar Haddad & Ilyas Kecis & Lionel Thibault, 2015. "Reduction of state dependent sweeping process to unconstrained differential inclusion," Journal of Global Optimization, Springer, vol. 62(1), pages 167-182, May.
    3. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, October.
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    Citations

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    Cited by:

    1. Fatine Aliouane & Dalila Azzam-Laouir & Charles Castaing & Manuel D. P. Monteiro Marques, 2019. "Second-Order Time and State-Dependent Sweeping Process in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 153-188, July.
    2. Giovanni Colombo & Boris Mordukhovich & Dao Nguyen, 2019. "Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 439-472, August.
    3. Shengda Zeng & Emilio Vilches, 2020. "Well-Posedness of History/State-Dependent Implicit Sweeping Processes," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 960-984, September.
    4. Diana Narváez & Emilio Vilches, 2022. "Moreau–Yosida Regularization of Degenerate State-Dependent Sweeping Processes," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 910-930, June.

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