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

Xuan Duc Ha Truong (txdha***at***math.ac.vn)

Abstract: 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.

Keywords: Set-valued map; slope; set optimization; error bound; optimal solution; Palais-Smale condition

Category 1: Other Topics (Multi-Criteria Optimization )

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

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Entry Submitted: 07/19/2018
Entry Accepted: 07/19/2018
Entry Last Modified: 07/23/2019

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