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Moreau–Yosida Regularization of Degenerate State-Dependent Sweeping Processes

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Abstract

In this paper, we introduce and study degenerate state-dependent sweeping processes with nonregular moving sets (subsmooth and positively \(\alpha \)-far). Based on the Moreau–Yosida regularization, we prove the existence of solutions under the Lipschitzianity of the moving sets with respect to the truncated Hausdorff distance.

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Acknowledgements

The authors wish to thank the referees for providing several helpful suggestions. Diana Narváez was supported by Centro de Modelamiento Matemático (CMM), ACE210010 and FB210005, BASAL funds for center of excellence, Fondecyt Regular N\(^{\circ }\) 1171854, and Fondecyt Regular N\(^{\circ }\) 1190012 from ANID-Chile. Emilio Vilches was supported by Centro de Modelamiento Matemático (CMM), ACE210010 and FB210005, BASAL funds for center of excellence, Fondecyt de Iniciación N\(^{\circ }\) 11180098 and Fondecyt Regular 1200283 from ANID-Chile.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile

    Diana Narváez

  2. Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

    Diana Narváez & Emilio Vilches

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  1. Diana Narváez
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  2. Emilio Vilches
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Correspondence to Emilio Vilches.

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Communicated by Boris S. Mordukhovich.

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Narváez, D., Vilches, E. Moreau–Yosida Regularization of Degenerate State-Dependent Sweeping Processes. J Optim Theory Appl 193, 910–930 (2022). https://doi.org/10.1007/s10957-022-02030-1

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