A Generalized Scalarization Method in Set Optimization with Respect to Variable Domination Structures

Ait Mansour, M., Durea, M., Théra, M.: A lower semicontinuous regularization for set-valued mappings and its applications. J. Convex Anal. 15, 473–484 (2008)

Bouza, G., Tammer, Chr: Nonlinear scalarizing functions for computing minimal points under variable ordering structures. Appl. Anal. Optim. 1, 67–97 (2017)

Ernst, E., Théra, M.: On the necessity of the Moreau–Rockafellar–Robinson qualification condition in Banach spaces. Math. Program. Ser. B 117, 149–161 (2009)

Eichfelder, G.: Variable Ordering Structures in Vector Optimization. Springer, Heidelberg (2014)

Eichfelder, G., Pilecka, M.: Set approach for set optimization with variable ordering structures Part I: set relations and relationship to vector approach. J. Optim. Theory Appl. 171, 931–946 (2016)

Eichfelder, G., Pilecka, M.: Set approach for set optimization with variable ordering structures Part II: scalarization approaches. J. Optim. Theory Appl. 171, 947–963 (2016)

Eichfelder, G.: Optimal elements in vector optimization with a variable ordering structure. J. Optim. Theory Appl. 151, 217–240 (2011)

Gutiérrez, C., Jiménez, B., Miglierina, E., Molho, E.: Scalarization in set optimization with solid and nonsolid ordering cones. J. Glob. Optim. 61, 525–552 (2015)

Gutiérrez, C., Miglierina, E., Molho, E., Novo, V.: Pointwise well-posedness in set optimization with cone proper sets. Nonlinear Anal. 75, 1822–1833 (2012)

Göpfert, A., Tammer, Chr, Riahi, H., Zǎlinescu, C.: Variational Methods in Partially Ordered Spaces. Springer-Verlag, Berlin (2003)

Gerth (Tammer), Chr, Weidner, P.: Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67, 297–320 (1990)

Heyde, F.: Coherent risk measures and vector optimization. In: Küfer, K.-H., et al. (eds.) Multicriteria Decision Making and Fuzzy Systems. Theory, Methods and Applications, pp 3–12. Shaker-Verlag, Aachen (2006)

Huynh, V.N., Théra, M.: Directional metric regularity of multifunctions. Math. Oper. Res. 40, 969–991 (2015)

Jahn, J.: Vectorization in set optimization. J. Optim. Theory Appl. 167, 783–795 (2015)

Jahn, J.: A derivative-free descent method in set optimization. Comput. Optim. Appl. 60, 393–411 (2015)

Khan, A.A., Tammer, Chr, Zălinescu, C.: Set-Valued Optimization: An Introduction with Applications. Springer, Berlin (2015)

Köbis, E., Köbis, M.A.: Treatment of set order relations by means of a nonlinear scalarization functional: A full characterization. Optimization 65, 1805–1827 (2016)

Köbis, E.: Variable ordering structures in set optimization. Preprint 378, University Erlangen-Nürnberg (2014)

Köbis, E., Tammer, Chr: Characterization of set relations by means of a nonlinear scalarization functional. In: Hoai An, L.T., et al. (eds.) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol. 359, pp. 491–503. Springer (2015)

Köbis, E., Le, T.T., Tammer, Chr: Necessary optimality conditions for solutions of set optimization with respect to variable domination structures. Reports on Optimization and Stochastics 04–2017 (2017)

Ngai, H.V., Tron, N.H., Théra, M.: Metric regularity of the sum of multifunctions and applications. J. Optim. Theory Appl. 160, 355–390 (2014)

Ngai, H.V., Kruger, A.Y., Théra, M.: Slopes of multifunctions and extensions of metric regularity. Vietnam J. Math. 40, 355–369 (2012)

Wacker, M.: Multikriterielle Optimierung bei Registrierung medizinischer Daten. Friedrich-Alexander-University Erlangen-Nuremberg, Master thesis (2008)

Weidner, P.: Ein Trennungskonzept und seine Anwendung auf Vektoroptimierungsverfahren. Martin-Luther-Universität Halle-Wittenberg, Dissertation B (1990)