Well-Posedness and Inf-Convolution

Mohammed Bachir (1, 2)

1 Equations d'evolution
2 UP1 - Université Paris 1 Panthéon-Sorbonne

We prove that the notion of Tykhonov well-posed problems is stable under the operation of inf-convolution. We deal with lower semicontinuous functions (not necessarily convex) defined on a metric magma. Several applications are given, in particular to the study of the map argmin.

Keywords: Invariant metric group and magma; Inf-convolution; Tykhonov well-posed problems; 1-Lipschitz function

Domains: Mathematics [math]; Functional Analysis [math.FA]

Mohammed Bachir. Well-Posedness and Inf-Convolution. Journal of Optimization Theory and Applications, 2018, 177 (2), pp.271-290. ⟨hal-01768179⟩