Geodesic
Perturbed Degenerate State-Dependent Sweeping Processes with Convex and Nonconvex Sets
Journal of convex analysis, Tome 31 (2024) no. 1, pp. 59-74
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We prove by means of the Moreau-Yosida regularization an existence result for perturbed degenerate state-dependent sweeping processes with convex and nonconvex moving sets. The moving sets vary in a Lipschitz continuous way with respect to the truncated Hausdorff distance. The theoretical results are applied to obtain the well-posedness for the online mirror descent method. The novelty of this work lies in the introduction of new local arguments for the Moreau-Yosida regularization that allow us to obtain the existence of solutions in small intervals and then pass to any interval.
Classification : 34G25, 49J52, 49J53
Mots-clés : Sweeping Processes, normal cone, mirror descent method, subsmooth sets, Moreau-Yosida regularization 
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     author = {D. Narv\'aez and E. Vilches},
     title = {Perturbed {Degenerate} {State-Dependent} {Sweeping} {Processes} with {Convex} and {Nonconvex} {Sets}},
     journal = {Journal of convex analysis},
     pages = {59--74},
     year = {2024},
     volume = {31},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2024_31_1_JCA_2024_31_1_a4/}
}
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D. Narváez; E. Vilches. Perturbed Degenerate State-Dependent Sweeping Processes with Convex and Nonconvex Sets. Journal of convex analysis, Tome 31 (2024) no. 1, pp. 59-74. http://geodesic.mathdoc.fr/item/JCA_2024_31_1_JCA_2024_31_1_a4/