A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa’s set approach

摘要

titleAbstract/titlepIn this paper, we introduce a new concept of slope for a set-valued map using a scalarizing function defined with the help of the Hiriart-Urruty signed distance function. It turns out that this slope possesses most properties of the strong slope of a scalar-valued function. We present some applications in set optimization studied with Kuroiwa’s set approach. Namely, we obtain criteria for error bounds of a lower level set and the existence of weak optimal solutions under a Palais–Smale type condition./p