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

In this paper, scalarizing functions defined with the help of the Hiriart-Urruty signed distance are used to characterize set order relations and weak optimal solutions in set optimization studied with Kuroiwa's set approach and to introduce a new concept of slope for a set-valued map. It turns out that this slope possesses most properties of the strong slope of a scalar-valued function. As applications, we obtain criteria for error bounds of a lower level set and the existence of weak optimal solutions under a Palais-Smale type condition.


To appear in Mathematical Methods of Operation Research DOI: 10.1007/s00186-019-00676-8