On the stability of minimal solutions for parametric set optimization problems

References

• Alonso M, Rodríguez-Marín L. Set-relations and optimality conditions in set-valued maps. Nonlinear Anal. 2005;63:1167–1179. doi: 10.1016/j.na.2005.06.002
   Web of Science ®Google Scholar
• Bao TQ, Mordukhovich BS. Relative Pareto minimizers for multiobjective problems: existence and optimality conditions. Math Program Ser A. 2010;122:301–347. doi: 10.1007/s10107-008-0249-2
   Web of Science ®Google Scholar
• Chen GY, Huang XX, Yang XQ. Vector optimization: set-valued and variational analysis. Berlin: Springer; 2005. (Lectures Notes in Economics and Mathematical Systems, vol. 514).
   Google Scholar
• Huang NJ, Li J, Thompson HB. Stability for parametric implicit vector equilibrium problems. Math Comput Model. 2006;43:1267–1274. doi: 10.1016/j.mcm.2005.06.010
   Web of Science ®Google Scholar
• Hernández E, Rodríguez-Marín L. Nonconvex scalarization in set optimization with set-valued maps. J Math Anal Appl. 2007;325:1–18. doi: 10.1016/j.jmaa.2006.01.033
   Web of Science ®Google Scholar
• Jahn J, Ha TXD. New set relations in set optimization. J Optim Theory Appl. 2011;148:209–236. doi: 10.1007/s10957-010-9752-8
   Web of Science ®Google Scholar
• Kien BT, Tuyen NV, Yao JC. Second-order KKT optimality conditions for multiobjective optimal control problems. SIAM J Control Optim. 2018;56:4069–4097. doi: 10.1137/17M1161750
   Web of Science ®Google Scholar
• Khan AA, Tammer C, Zlinescu C. Set-valued optimization. Heidelberg: Springer; 2015.
   Google Scholar
• Kuroiwa D. On set-valued optimization. Nonlinear Anal. 2001;47:1395–1400. doi: 10.1016/S0362-546X(01)00274-7
   Web of Science ®Google Scholar
• Kuroiwa D. Existence theorems of set optimization with set-valued maps. J Inf Optim Sci. 2003;24:73–84.
   Google Scholar
• Li J, Tammer C. Set optimization problems on ordered sets. Appl Set-Valued Anal Optim. 2019;1:77–94.
   Google Scholar
• Tung LT. Karush-Kuhn-Tucker optimality conditions for nonsmooth multiobjective semidefinite and semi-infinite programming. J Appl Numer Optim. 2019;1:63–75.
   Google Scholar
• Van Tuyen N, Yao JC, Wen CF. A note on approximate Karush-Kuhn-Tucker conditions in locally Lipschitz multiobjective optimization. Optim Lett. 2019;13:163–174. doi: 10.1007/s11590-018-1261-y
   Web of Science ®Google Scholar
• Yao JC, Zheng XY. Existence of solutions and error bound for vector variational inequalities in Banach spaces. Optimization. 2018;67:1333–1344. doi: 10.1080/02331934.2018.1429433
   Web of Science ®Google Scholar
• Dhingra M, Lalitha CS. Set optimization using improvement sets. Yugosl J Oper Res. 2017;27:153–167. doi: 10.2298/YJOR170115011D
   Google Scholar
• Geoffroy MH, Marcelin Y, Nedelcheva D. Convergence of relaxed minimizers in set optimization. Optim Lett. 2017;11:1677–1690. doi: 10.1007/s11590-016-1079-4
   Web of Science ®Google Scholar
• Karuna, Lalitha CS. External and internal stability in set optimization. Optimization. 2019;68:833–852. doi: 10.1080/02331934.2018.1556663
   Web of Science ®Google Scholar
• Xu YD, Li SJ. Continuity of the solution set mappings to a parametric set optimization problem. Optim Lett. 2014;8:2315–2327. doi: 10.1007/s11590-014-0738-6
   Web of Science ®Google Scholar
• Xu YD, Li SJ. On the solution continuity of parametric set optimization problems. Math Meth Oper Res. 2016;84:223–237. doi: 10.1007/s00186-016-0541-5
   Web of Science ®Google Scholar
• Han Y, Huang NJ. Well-posedness and stability of solutions for set optimization problems. Optimization. 2017;66:17–33. doi: 10.1080/02331934.2016.1247270
   Web of Science ®Google Scholar
• Khoshkhabar-amiranloo S. Stability of minimal solutions to parametric set optimization problems. Appl Anal. 2018;97:2510–2522. doi: 10.1080/00036811.2017.1376320
   Web of Science ®Google Scholar
• Han Y, Huang NJ. Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications. J Optim Theory Appl. 2018;177:679–695. doi: 10.1007/s10957-017-1080-9
   Web of Science ®Google Scholar
• Geoffroy MH. A topological convergence on power sets well-suited for set optimization. J Global Optim. 2019;73:567–581. doi: 10.1007/s10898-018-0712-4
   Web of Science ®Google Scholar
• 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. doi: 10.1080/02331934.2018.1454920
   Web of Science ®Google Scholar
• Aubin JP, Ekeland I. Applied nonlinear analysis. New York (NY): Wiley; 1984.
   Google Scholar
• Göpfert A, Riahi H, Tammer C, Zlinescu C. Variational methods in partially ordered spaces. Berlin: Springer; 2003.
   Google Scholar