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

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  • Truong Xuan Duc Ha

    (Thanglong University)

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.

Suggested Citation

  • Truong Xuan Duc Ha, 2020. "A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa’s set approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 137-158, February.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:1:d:10.1007_s00186-019-00676-8
    DOI: 10.1007/s00186-019-00676-8
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