Semi-continuity of the solution maps of set-valued equilibrium problems with equilibrium constraints

References

• Ansari QH, Köbis E, Yao J-C. Vector variational inequalities and vector optimization: theory and applications. Berlin: Springer International Publishing AG; 2018.
   Google Scholar
• Ansari QH, Oettli W, Schläger D. A generalization of vectorial equilibria. Math Meth Oper Res. 1997;46:147–152. doi: 10.1007/BF01217687
   Web of Science ®Google Scholar
• Ansari QH, Schaible S, Yao JC. Generalized vector equilibrium problems under generalized pseudomonotonicity with applications. J Nonlinear Convex Anal. 2002;3(3):331–344.
   Google Scholar
• Araya Y, Saito Y, Kimura Y. On some extended formulations of vector equilibrium problem and its existence theorems. J Nonlinear Convex Anal. 2021;22(5):925–935.
   Web of Science ®Google Scholar
• Lin L-J, Ansari QH, Wu CY. Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems. J Optim Theory Appl. 2003;117(1):121–137. doi: 10.1023/A:1023656507786
   Web of Science ®Google Scholar
• Anh LQ, Duoc PT, Tam TN, et al. Stability analysis for set-valued equilibrium problems with applications to Browder variational inclusions. Optim Lett. 2021;15:613–626. doi: 10.1007/s11590-020-01604-0
   Web of Science ®Google Scholar
• Kimura K, Yao JC. Semicontinuity of solution mappings of parametric generalized vector equilibrium problems. J Optim Theory Appl. 2008;138:429–443. doi: 10.1007/s10957-008-9386-2
   Web of Science ®Google Scholar
• Capata A. Existence of solutions of bilevel strong vector equilibrium problems and their applications. J Nonlinear Var Anal. 2021;5:371–389.
   Web of Science ®Google Scholar
• Kimura K, Liou YC, Wu SY, et al. Well-posedness for parametric vector equilibrium problems with applications. J Ind Manag Optim. 2008;4(2):313–327. doi: 10.3934/jimo.2008.4.313
   Google Scholar
• Han Y, Huang NJ. The connectedness of the solutions set for generalized vector equilibrium problems. Optimization. 2016;65(2):357–367. doi: 10.1080/02331934.2015.1044899
   Web of Science ®Google Scholar
• Alleche B, Rădulescu VD. Further on set-valued equilibrium problems and applications to Browder variational inclusions. J Optim Theory Appl. 2017;175:39–58. doi: 10.1007/s10957-017-1169-1
   Web of Science ®Google Scholar
• Alleche B, Rădulescu VD. Further on set-valued equilibrium problems in the pseudo-monotone case and applications to Browder variational inclusions. Optim Lett. 2018;12:1789–1810. doi: 10.1007/s11590-018-1233-2
   Web of Science ®Google Scholar
• Chen B, Gong XH. Continuity of the solution set to parametric set-valued weak vector equilibrium problems. Pacific J Optim. 2010;6(3):511–520.
   Web of Science ®Google Scholar
• Chen B, Huang NJ. Continuity of the solution mapping to parametric generalized vector equilibrium problems. J Global Optim. 2013;56(4):1515–1528. doi: 10.1007/s10898-012-9904-5
   Web of Science ®Google Scholar
• Chen CR, Li SL, Teo TL. Solution semicontinuity of parametric generalized vector equilibrium problems. J Global Optim. 2009;45(2):309–318. doi: 10.1007/s10898-008-9376-9
   Web of Science ®Google Scholar
• Darabi M, Zafarani J. Hadamard well-posedness for vector parametric equilibrium problems. J Nonlinear Var Anal. 2017;1:281–295.
   Web of Science ®Google Scholar
• Li J. Constrained ordered equilibrium problems and applications. J Nonlinear Var Anal. 2017;1:357–365.
   Web of Science ®Google Scholar
• Anh LQ. Semicontinuity of the solution maps to vector quilibrium problems with equilibrium constraints. Optimization. 2022;71(3):737–751. doi: 10.1080/02331934.2020.1812067
   Web of Science ®Google Scholar
• Zhao Y, Peng ZY, Yang XM. Semicontinuity and convergence for vector optimization problems with approximate equilibrium constraints. Optimization. 2016;65(7):1397–1415. doi: 10.1080/02331934.2016.1149711
   Web of Science ®Google Scholar
• Ansari QH, Sharma PK. Set order relations, set optimization, and Ekeland's variational principle In: Laha V, Maréchal P, Mishra SK, editors. Optimization, variational analysis and applications. Springer Nature Singapore Pvt. Ltd; 2021. p. 103–165. (Springer proceedings in mathematics & statistics; vol. 355).
   Google Scholar
• Ansari QH, Sharma PK, Yao J-C. Minimal elements theorems and Ekeland's variational principle with new set order relations. J Nonlinear Convex Anal. 2018;19(7):1127–1139.
   Web of Science ®Google Scholar
• Jahn J, Ha TXD. New order relations in set optimization. J Optim Theory Appl. 2011;148:209–236. doi: 10.1007/s10957-010-9752-8
   Web of Science ®Google Scholar
• Kuroiwa D. Some criteria in set-valued optimization. Sūrikaisekikenkyūsho Kōkyūroku. 1997;985:171–176.
   Google Scholar
• Khan AA, Tammer C., Zălinescu C. Set-valued optimization – an introduction with applications. Berlin, Heidelberg: Springer; 2015.
   Google Scholar
• Aubin JP, Ekeland I. Applied nonlinear analysis. New York: Wiley; 1984.
   Google Scholar
• Hu S, Papageorgiou N. Handbook of multivalued analysis, volume I: theory. Boston: Kluwer; 1997.
   Google Scholar
• Lin LJ, Wang SY, Chuang CS. Existence theorems of systems of variational inclusion problems with applications. J Glob Optim. 2008;40:751–764. doi: 10.1007/s10898-007-9160-2
   Web of Science ®Google Scholar
• Balaj M, Lin LJ. Generalized variational relation problems with applications. J Optim Theory Appl. 2011;148:1–13. doi: 10.1007/s10957-010-9741-y
   Web of Science ®Google Scholar
• Lin Y-C, Ansari QH, Lai H-C. Minimax theorems for set-valued mappings under cone-convexities. Abstr Appl Anal. 2012;2012:310818.
   Google Scholar
• Ansari QH, Flores-Bazan F. Recession method for generalized vector equilibrium problems. J Math Anal Appl. 2006;321(1):132–146. doi: 10.1016/j.jmaa.2005.07.059
   Web of Science ®Google Scholar
• Balaj M, Serac DF. Equilibrium problems when the equilibrium condition is missing. Arab J Math. 2023;12:331–340. doi: 10.1007/s40065-023-00428-x
   Web of Science ®Google Scholar
• Glicksberg IL. A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points. Proc Am Math Soc. 1952;3(1):170–174.
   Web of Science ®Google Scholar
• Fan XD, Cheng CZ, Wang HJ. Sensitivity analysis for vector equilibrium problems under functional perturbation. Numer Funct Anal Optim. 2014;35:564–575. doi: 10.1080/01630563.2013.814140
   Web of Science ®Google Scholar
• Gong XH. Continuity of the solution set to parametric weak vector equilibrium problems. J Optim Theory Appl. 2008;139:35–46. doi: 10.1007/s10957-008-9429-8
   Web of Science ®Google Scholar
• Gong XH, Yao JC. Lower semicontinuity of the set of efficient solutions for generalized systems. J Optim Theory Appl. 2008;138:197–205. doi: 10.1007/s10957-008-9379-1
   Web of Science ®Google Scholar