Open Access
Issue |
RAIRO-Oper. Res.
Volume 59, Number 2, March-April 2025
|
|
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Page(s) | 1019 - 1034 | |
DOI | https://doi.org/10.1051/ro/2025025 | |
Published online | 21 April 2025 |
- L.Q. Anh, T.Q. Duy and D.V. Hien, Stability of efficient solutions to set optimization problems. J. Global Optim. 78 (2020) 563–580. [CrossRef] [MathSciNet] [Google Scholar]
- L.Q. Anh, T.Q. Duy, D.V. Hien, D. Kuroiwa and N. Petrot, Convergence of solutions to set optimization problems with the set less order relation. J. Optim. Theory Appl. 185 (2020) 416–432. [CrossRef] [MathSciNet] [Google Scholar]
- L.Q. Anh, N.H. Danh, P.T. Duoc and T.N. Tam, Qualitative properties of solutions to set optimization problems. Comp. Appl. Math. 40 (2021) 1–18. [CrossRef] [Google Scholar]
- L.Q. Anh, P.T. Duoc and T.T.T. Duong, A new scalarization approach and applications in set optimization. Optimization 72 (2023) 1093–1117. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Araya, Four types of nonlinear scalarizations and some applications in set optimization. Nonlinear Anal. 75 (2012) 3821–3835. [CrossRef] [MathSciNet] [Google Scholar]
- T.Q. Bao and C. Tammer, Scalarization functionals with uniform level sets in set optimization. J. Optim. Theory Appl. 182 (2019) 310–335. [CrossRef] [MathSciNet] [Google Scholar]
- H. Corley, Optimality conditions for maximizations of set-valued functions. J. Optim. Theory Appl. 58 (1988) 1–10. [CrossRef] [MathSciNet] [Google Scholar]
- S. Dempe and M. Pilecka, Optimality conditions for set-valued optimisation problems using a modified demyanov difference. J. Optim. Theory Appl. 171 (2016) 402–421. [CrossRef] [MathSciNet] [Google Scholar]
- C. Gerstewitz, Nichtkonvexe dualit¨at in der vektoroptimierung. Wiss. Z. Tech. Hochsch. Leuna-Merseburg 25 (1983) 357–364. [MathSciNet] [Google Scholar]
- C. Gerth and P. Weidner, Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67 (1990) 297–320. [CrossRef] [MathSciNet] [Google Scholar]
- A. Göpfert, H. Riahi, C. Tammer and C. Zalinescu, Variational Methods in Partially Ordered Spaces. Vol. 17. Springer, Berlin (2003). [Google Scholar]
- A. Götz and J. Jahn, The lagrange multiplier rule in set-valued optimization. SIAM J. Optim. 10 (2000) 331–344. [CrossRef] [MathSciNet] [Google Scholar]
- C. Gutiérrez, B. Jiménez, E. Miglierina and E. Molho, Scalarization in set optimization with solid and nonsolid ordering cones. J. Global Optim. 61 (2015) 525–552. [CrossRef] [MathSciNet] [Google Scholar]
- C. Gutiérrez, L. Huerga, E. Köbis and C. Tammer, A scalarization scheme for binary relations with applications to set-valued and robust optimization. J. Global Optim. 79 (2021) 233–256. [CrossRef] [MathSciNet] [Google Scholar]
- T.X.D. Ha, A hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization. Optimization 67 (2018) 1031–1050. [CrossRef] [MathSciNet] [Google Scholar]
- T.X.D. Ha, A new concept of slope for set-valued maps and applications in set optimization studied with kuroiwas set approach. Math. Methods Oper Res. 91 (2020) 137–158. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Han, A hausdorff-type distance, the clarke generalized directional derivative and applications in set optimization problems. Appl. Anal. 101 (2022) 1243–1260. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Han, Directional derivative and subgradient of cone-convex set-valued mappings with applications in set optimization problems. J. Oper. Res. Soc. Chin. 12 (2024) 1103–1125. [CrossRef] [Google Scholar]
- Y. Han, N.-J. Huang and C.-F. Wen, A set scalarization function and dini directional derivatives with applications in set optimization problems. J. Nonlinear Var. Anal. 5 (2021) 909–927. [Google Scholar]
- E. Hernández and L. Rodríguez-Marín, Existence theorems for set optimization problems. Nonlinear Anal. 67 (2007) 1726–1736. [CrossRef] [MathSciNet] [Google Scholar]
- E. Hernández, L. Rodríguez-Marín and M. Sama, On solutions of set-valued optimization problems. Comp. Math. Appl. 60 (2010) 1401–1408. [CrossRef] [Google Scholar]
- L. Huerga, B. Jiménez, V. Novo and A. Vílchez, Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization. Math. Methods Oper. Res. 93 (2021) 413–436. [CrossRef] [MathSciNet] [Google Scholar]
- J. Ide, E. Köbis, D. Kuroiwa, A. Schöbel and C. Tammer, The relationship between multi-objective robustness concepts and set-valued optimization. Fix. Point Theory Appl. 2014 (2014) 1–20. [CrossRef] [Google Scholar]
- J. Jahn, Directional derivatives in set optimization with the set less order relation. Taiwanese J. Math. 19 (2015) 737–757. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jahn, Vector Optimization. Springer, Berlin (2009). [Google Scholar]
- J. Jahn and T.X.D. Ha, New order relations in set optimization. J. Optim. Theory Appl. 148 (2011) 209–236. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jahn, A. Khan and P. Zeilinger, Second-order optimality conditions in set optimization. J. Optim. Theory Appl. 125 (2005) 331–347. [CrossRef] [MathSciNet] [Google Scholar]
- B. Jiménez, V. Novo and A. Vílchez, Six set scalarizations based on the oriented distance: properties and application to set optimization. Optimization 69 (2020) 437–470. [CrossRef] [MathSciNet] [Google Scholar]
- A.A. Khan and C. Tammer, Second-order optimality conditions in set-valued optimization via asymptotic derivatives. Optimization 62 (2013) 743–758. [CrossRef] [MathSciNet] [Google Scholar]
- A.A. Khan, C. Tammer and C. Zalinescu, Set-valued Optimization. Springer, Berlin (2016). [Google Scholar]
- P.Q. Khanh and N.M. Tung, Second-order optimality conditions with the envelope-like effect for set-valued optimization. J. Optim. Theory Appl. 167 (2015) 68–90. [CrossRef] [MathSciNet] [Google Scholar]
- S. Khoshkhabar-Amiranloo and E. Khorram, Scalar characterizations of cone-continuous set-valued maps. Appl. Anal. 95 (2016) 2750–2765. [CrossRef] [MathSciNet] [Google Scholar]
- K. Klamroth, E. Köbis, A. Schöbel and C. Tammer, A unified approach to uncertain optimization. Eur. J. Oper. Res. 260 (2017) 403–420. [CrossRef] [Google Scholar]
- D. Kuroiwa, Convexity for set-valued maps. Appl. Math. Lett. 9 (1996) 97–101. [CrossRef] [MathSciNet] [Google Scholar]
- D. Kuroiwa, The natural criteria in set-valued optimization. Nonlinear Anal. Conv. Anal. 1031 (1998) 85–90. [Google Scholar]
- S. Li, K. Teo and X. Yang, Higher-order optimality conditions for set-valued optimization. J. Optim. Theory Appl. 137 (2008) 533–553. [CrossRef] [MathSciNet] [Google Scholar]
- D.T. Luc, Theory of Vector Optimization. Springer, Berlin (1989). [Google Scholar]
- Z. Nishnianidze, Fixed points of monotonic multiple-valued operators. Bull. Georgian Acad. Sci. 114 (1984) 489–491. [Google Scholar]
- R.T. Rockafellar, Convex Analysis. Vol. 18. Princeton University Press, Jersey (1970). [Google Scholar]
- W. Rudin, Functional Analysis. McGraw-Hill, New York (1991). [Google Scholar]
- R.C. Young, The algebra of many-valued quantities. Math. Ann. 104 (1931) 260–290. [CrossRef] [MathSciNet] [Google Scholar]
- C. Zalinescu, Convex Analysis in General Vector Spaces. World Scientific (2002). [Google Scholar]
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