Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 67, 2018 - Issue 12
74
Views
4
CrossRef citations to date
0
Altmetric
Articles

Cyclically antimonotone vector equilibrium problems

Pages 2191-2204 | Received 10 Apr 2018, Accepted 06 Sep 2018, Published online: 21 Sep 2018

References

  • Ekeland I. Sur les problèmes variationnels. C R Acad Sci Paris. 1972;275:1057–1059.
  • Tammer Chr.. A generalization of Ekeland's variational principle. Optimization. 1992;25(2-3):129–141. doi: 10.1080/02331939208843815
  • Oettli W, Théra M. Equivalents of Ekeland's principle. Bull Austral Math Soc. 1993;48(3):385–392. doi: 10.1017/S0004972700015847
  • Chen GY, Huang XX. Stability results for Ekeland's ϵ variational principle for vector valued functions. Math Methods Oper Res. 1998;48(1):97–103. doi: 10.1007/s001860050014
  • Ansari QH. Vector equilibrium problems and vector variational inequalities: mathematical theories. In: Giannessi F, editor. Chapter Vector variational inequalities and vector equilibria. Dordrecht: Kluwer Acad. Publ.; 2000. p. 1–15.
  • Göpfert A, Tammer Chr, Zalinescu C. On the vectorial Ekeland's variational principle and minimal points in product spaces. Nonlinear Anal. 2000;39(7):909–922. doi: 10.1016/S0362-546X(98)00255-7
  • Ansari QH, Yang XQ, Yao J-C. Existence and duality of implicit vector variational problems. Numer Funct Anal Optim. 2001;22(7-8):815–829. doi: 10.1081/NFA-100108310
  • Ansari QH, Konnov IV, Yao J-C. On generalized vector equilibrium problems. Nonlinear Anal. 2001;47(1):543–554. doi: 10.1016/S0362-546X(01)00199-7
  • Ansari QH. Vectorial form of Ekeland-type variational principle with applications to vector equilibrium problems and fixed point theory. J Math Anal Appl. 2007;334(1):561–575. doi: 10.1016/j.jmaa.2006.12.076
  • Bianchi M, Kassay G, Pini R. Ekeland's principle for vector equilibrium problems. Nonlinear Anal. 2007;66(7):1454–1464. doi: 10.1016/j.na.2006.02.003
  • Al-Homidan S, Ansari QH, Yao J-C. Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory. Nonlinear Anal. 2008;69(1):126–139. doi: 10.1016/j.na.2007.05.004
  • Araya Y, Kimura K, Tanaka T. Existence of vector equilibria via Ekeland's variational principle. Taiwanese J Math. 2008;12(8):1991–2000. doi: 10.11650/twjm/1500405131
  • Ansari QH. Ekeland's variational principle and its extensions with applications. In: Almezel S., Ansari Q.H., Khamsi M.A., editors. Chapter Topics in fixed point theory. Cham: Springer; 2014; p. 65–100.
  • Gutiérrez C, Kassay G, Novo V, et al. Ekeland variational principles in vector equilibrium problems. SIAM J Optim. 2017;27(4):2405–2425. doi: 10.1137/17M111883X
  • Castellani M, Giuli M. Ekeland's principle for cyclically antimonotone equilibrium problems. Nonlinear Anal Real World Appl. 2016;32:213–228. doi: 10.1016/j.nonrwa.2016.04.011
  • Borwein JM, Penot J-P, Théra M. Conjugate convex operators. J Math Anal Appl. 1984;102(2):399–414. doi: 10.1016/0022-247X(84)90180-X
  • Théra M. Étude des fonctions convexes vectorielles semicontinues, Thèse de cycle. Pau: Université de Pau; 1978.
  • Finet C, Quarta L, Troestler C. Vector-valued variational principles. Nonlinear Anal. 2003;52(1):197–218. doi: 10.1016/S0362-546X(02)00103-7
  • Luc DT. Theory of vector optimization. Berlin: Springer-Verlag; 1989.
  • Löhne A. Vector optimization with infimum and supremum. Heidelberg: Springer; 2011.
  • Aliprantis CD, Border KC. Infinite dimensional analysis. A Hitchhiker's Guide. Berlin: Springer; 2006.

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.