312
Views
3
CrossRef citations to date
0
Altmetric
Articles

New concepts of directional derivatives for set-valued maps and applications to set optimization

, &
Pages 1069-1091 | Received 21 Oct 2021, Accepted 04 Jun 2022, Published online: 16 Jun 2022

References

  • Hamel AH, Heyde F, Löhne A. Set optimization and applications – the state of the art. Berlin: Springer; 2015.
  • Khan AA, Tammer C, Zălinescu C. Set-valued optimization: an introduction with applications. Heidelberg: Springer; 2015.
  • Jiménez B, Novo V, Vílchez A. Characterization of set relations through extensions of the oriented distance. Math Methods Oper Res. 2020;91:89–115.
  • Seto K, Kuroiwa D, Popovici N. A systematization of convexity and quasiconvexity concepts for set-valued maps defined by l-type and u-type preorder relations. Optimization. 2018;67:1077–1094.
  • Khoshkhabar-amiranloo S. Characterizations of generalized Levitin–Polyak well-posed set optimization problems. Optim Lett. 2019;13:147–161.
  • Khushboo T, Lalitha CS. A unified minimal solution in set optimization. J Global Optim. 2019;74:195–211.
  • Vui PT, Anh LQ, Wangkeeree R. Levitin–Polyak well-posedness for set optimization problems involving set order relations. Positivity. 2019;23:599–616.
  • Zhang CL, Zhou LW, Huang NJ. Stability of minimal solution mappings for parametric set optimization problems with pre-order relations. Pacific J Optim. 2019;15:491–504.
  • Han Y, Huang N-J, Wen C-F. A set scalarization function and Dini directional derivatives with applications in set optimization problems. J Nonlinear Variational Anal. 2021;5:909–927.
  • Schmidt KD. Embedding theorems for classes of convex sets. Acta Appl Math. 1986;5:209–237.
  • Kuroiwa D, Nuriya T. A generalized embedding vector space in set optimization. In: Proceedings of the Forth International Conference on Nonlinear and Convex Analysis. Yokohama: Yokohama Publishers; 2006. p. 297–303.
  • Köbis E, Tam Le T, Tammer C. A generalized scalarization method in set optimization with respect to variable domination structures. Vietnam J Math. 2018;46:95–125.
  • Köbis E, Tam Le T, Tammer C, et al. Necessary conditions for solutions of set optimization problems with respect to variable domination structures. Pure Appl Functional Anal. 2019;4:317–343.
  • Sonntag Y, Zălinescu C. Set convergences: a survey and a classification. Set-Valued Anal. 1994;2:339–356.
  • Sonntag Y, Zălinescu C. Set convergences: an attempt of classification. Trans Am Math Soc. 1993;340:199–226.
  • Ha TXD. A hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization. Optimization. 2018;67:1031–1050.
  • Hernández E, Rodríguez-Marín L. Nonconvex scalarization in set optimization with set-valued maps. J Math Anal Appl. 2007;325:1–18.
  • Han Y, Huang NJ. Well-posedness and stability of solutions for set optimization problems. Optimization. 2017;66:17–33.
  • Dieudonné J. Sur la séparation des ensembles convexes. Mathematische Annalen. 1966;163:1–3.
  • Mordukhovich BS. Variational analysis and generalized differentiation. Berlin: Springer; 2006.
  • Luc DT. Theory of vector optimization. Berlin: Springer; 1989.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.