Well Posedness and Inf-Convolution

Mohammed Bachir ()
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Mohammed Bachir: Université Paris 1 Panthéon-Sorbonne, Centre P.M.F.

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 2, No 1, 290 pages

Abstract: Abstract 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 $$\arg \min $$ arg min .

Keywords: Inf-convolution; Tykhonov well-posed problems; 1-Lipschitz function; Invariant metric group and magma; 90C26; 65K10; 74P10 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1286-5

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