Abstract
The aim of this paper is to introduce two notions of Levitin$-$Polyak (LP in short) well-posedness for a parametric set optimization problem, a pointwise and a global notion. Necessary and sufficient conditions for a parametric set optimization problem to be LP well-posed are given. Characterizations of LP well-posedness for a parametric set optimization problem in terms of upper Hausdorff convergence and Painlev\'{e}$-$Kuratowski convergence of sequences of approximate solution sets are also established.
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