Robust efficiency and well-posedness in uncertain vector optimization problems

References

• Ehrgott M. Multicriteria optimization. Berlin: Springer; 2005.
   Google Scholar
• Ansari QH, Yao JC. Recent developments in vector optimization. Berlin: Springer; 2012.
   Google Scholar
• Birge JR, Louveaux F. Introduction to stochastic programming. Berlin: Springer; 2011.
   Google Scholar
• Adida E, Perakis G. Dynamic pricing and inventory control: robust vs. stochastic uncertainty models–a computational study. Ann Oper Res. 2010;181(1):125–157.
   Web of Science ®Google Scholar
• Beck A, Ben-Tal A. Duality in robust optimization: primal worst equals dual best. Oper Res Lett. 2009;37(1):1–6.
   Web of Science ®Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A. Robust optimization. London: Princeton University Press; 2009.
   Google Scholar
• Ben-Tal A, Goryashko A, Guslitzer E, et al. Adjustable robust solutions of uncertain linear programs. Math Program. 2004;99(2):351–376.
   Web of Science ®Google Scholar
• Goerigk M, Schöbel A. Recovery-to-optimality: a new two-stage approach to robustness with an application to aperiodic timetabling. Comput Oper Res. 2014;52:1–15.
   Web of Science ®Google Scholar
• Schöbel A. Generalized light robustness and the trade-off between robustness and nominal quality. Math Meth Oper Res. 2014;80(2):161–191.
   Web of Science ®Google Scholar
• Goerigk M, Schöbel A. A scenario-based approach for robust linear optimization. In: Marchetti-Spaccamela A, Segal M, editors. International conference on theory and practice of algorithms in (computer) systems; Berlin: Springer; 2011. p. 139–150.
   Google Scholar
• Kuroiwa D, Lee GM. On robust multiobjective optimization. Vietnam J Math. 2012;40(2–3):305–317.
   Google Scholar
• Georgiev PG, Luc DT, Pardalos PM. Robust aspects of solutions in deterministic multiple objective linear programming. Eur J Oper Res. 2013;229(1):29–36.
   Web of Science ®Google Scholar
• Kuhn K, Raith A, Schmidt M, et al. Bi-objective robust optimisation. Eur J Oper Res. 2016;252(2):418–431.
   Web of Science ®Google Scholar
• Botte M, Schöbel A. Dominance for multi-objective robust optimization concepts. Eur J Oper Res. 2019;273(2):430–440.
   Web of Science ®Google Scholar
• Sisarat N, Wangkeeree R, Lee GM. Some characterizations of robust solution sets for uncertain convex optimization problems with locally Lipschitz inequality constraints. J Ind Manag Optim. 2020;16(1):469–493.
   Web of Science ®Google Scholar
• Chuong TD. Robust optimality and duality in multiobjective optimization problems under data uncertainty. SIAM J Optim. 2020;30(2):1501–1526.
   Web of Science ®Google Scholar
• Kuroiwa D. The natural criteria in set-valued optimization. RIMS Kokyuroku Kyoto Univ. 1998;1031:85–90.
   Google Scholar
• Ehrgott M, Ide J, Schöbel A. Minmax robustness for multi-objective optimization problems. Eur J Oper Res. 2014;239(1):17–31.
   Web of Science ®Google Scholar
• Ide J, Köbis E, Kuroiwa D, et al. The relationship between multi-objective robustness concepts and set-valued optimization. Fix Point Theory Appl. 2014;2014(1):285.
   Google Scholar
• Eichfelder G, Krüger C, Schöbel A. Decision uncertainty in multiobjective optimization. J Glob Optim. 2017;69(2):485–510.
   Web of Science ®Google Scholar
• Ide J, Schöbel A. Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts. OR Spec. 2016;38(1):235–271.
   Web of Science ®Google Scholar
• Crespi GP, Kuroiwa D, Rocca M. Robust optimization: sensitivity to uncertainty in scalar and vector cases, with applications. Oper Res Perspect. 2018;5:113–119.
   Web of Science ®Google Scholar
• Bokrantz R, Fredriksson A. Necessary and sufficient conditions for pareto efficiency in robust multiobjective optimization. Eur J Oper Res. 2017;262(2):682–692.
   Web of Science ®Google Scholar
• Studniarski M, Michalak A, Stasiak A. Necessary and sufficient conditions for robust minimal solutions in uncertain vector optimization. J Optim Theory Appl. 2020;186(2):375–397.
   Web of Science ®Google Scholar
• Lee JH, Lee GM. On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems. Ann Oper Res. 2018;269(1–2):419–438.
   Web of Science ®Google Scholar
• Chen J, Köbis E, Yao JC. Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. J Optim Theory Appl. 2019;181(2):411–436.
   Web of Science ®Google Scholar
• Crespi GP, Kuroiwa D, Rocca M. Robust Nash equilibria in vector-valued games with uncertainty. Ann Oper Res. 2020;289:185–193.
   Web of Science ®Google Scholar
• Miglierina E, Molho E, Rocca M. Well-posedness and scalarization in vector optimization. J Optim Theory Appl. 2005;126(2):391–409.
   Web of Science ®Google Scholar
• Morgan J, Scalzo V. Discontinuous but well-posed optimization problems. SIAM J Optim. 2006;17(3):861–870.
   Web of Science ®Google Scholar
• Crespi GP, Papalia M, Rocca M. Extended well-posedness of vector optimization problems: the convex case. Taiwan J Math. 2011;15(4):1545–1559.
   Web of Science ®Google Scholar
• Anh LQ, Duy TQ, Kruger AY, et al. Well-posedness for lexicographic vector equilibrium problems. In: Demyanov VF, Pardalos P, Batsyn M, editors. Constructive nonsmooth analysis and related topics. New York (NY): Springer; 2014. p.159–174.
   Google Scholar
• Amini-Harandi A, Fakhar M, Hajisharifi HR. Some generalizations of the Weierstrass theorem. SIAM J Optim. 2016;26(4):2847–2862.
   Web of Science ®Google Scholar
• Anh LQ, Duy TQ. Tykhonov well-posedness for lexicographic equilibrium problems. Optimization. 2016;65(11):1929–1948.
   Web of Science ®Google Scholar
• Khoshkhabar-amiranloo S, Khorram E. Scalarization of Levitin–Polyak well-posed set optimization problems. Optimization. 2017;66(1):113–127.
   Web of Science ®Google Scholar
• Crespi GP, Dhingra M, Lalitha CS. Pointwise and global well-posedness in set optimization: a direct approach. Ann Oper Res. 2018;269(1–2):149–166.
   Web of Science ®Google Scholar
• Anh LQ, Duy TQ, Khanh PQ. Levitin–Polyak well-posedness for equilibrium problems with the lexicographic order. Positivity. 2021;25(4):1323–1349.
   Web of Science ®Google Scholar
• Duy TQ. Levitin–Polyak well-posedness in set optimization concerning pareto efficiency. Positivity. 2021;1–20. DOI:10.1007/s11117-021-00851-4.
   Web of Science ®Google Scholar
• Crespi GP, Kuroiwa D, Rocca M. Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization. Ann Oper Res. 2017;251(1–2):89–104.
   Web of Science ®Google Scholar
• Kuroiwa D, Nuriya T. A generalized embedding vector space in set optimization. In: Takahashi W, Tanaka T, editors. Proceedings of the forth international conference on nonlinear and convex analysis; Yokohama: Yokohama Publisher; 2006. p. 297–304.
   Google Scholar
• Anh LQ, Duy TQ, Hien DV. Well-posedness for the optimistic counterpart of uncertain vector optimization problems. Ann Oper Res. 2020;295(2):517–533.
   Web of Science ®Google Scholar
• Tanaka T. Generalized semicontinuity and existence theorems for cone saddle points. Appl Math Optim. 1997;36(3):313–322.
   Web of Science ®Google Scholar
• Khan AA, Tammer C, Zălinescu C. Set-valued optimization. Berlin: Springer; 2016.
   Google Scholar