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

Truong Xuan Duc Ha ()
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Truong Xuan Duc Ha: Thanglong University

Mathematical Methods of Operations Research, 2020, vol. 91, issue 1, No 8, 137-158

Abstract: Abstract In 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.

Keywords: Set-valued map; Slope; Set optimization; Error bound; Optimal solution; Palais–Smale condition (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-019-00676-8

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