[1] Adan, M. and Novo, V. Proper efficiency in vector optimization on real linear spaces, J. Optim. Theory Appl. 121 (2004), 515–540.
[2] Bao, T.Q., Mordukhovich, B.S. and Soubeyran, A. Variational analysis in psychological modeling, J. Optim. Theory Appl. 164 (2015), 290–315.
[3] Bazgan, C., Ruzika, S., Thielen, C. and Vanderpooten, D. The power of the weighted sum scalarization for approximating multiobjective opti-mization problems , Theory Comput. Syst. 66 (2022), 395–415.
[4] Benson, H.P. An improved definition of proper efficiency for vector max-imization with respect to cone, J. Math. Appl. 71 (1979), 232–241.
[5] Bergstresser, K., Charnes, A. and Yu, PL. Generalization of domination structures and nondominated solutions in multicriteria decision making, J. Optim. Theory Appl., 18 (1976), 3–13.
[6] Borwein, J.M. Proper efficient points for maximizations with respect to cones, SIAM J. Control Optim. 15 (1977), 57–63.
[7] Chen, G.Y. Existence of solutions for a vector variational inequality: an extension of the Hartmann Stampacchia theorem, J. Optim. Theory Appl. 74 (1992), 445–456.
[8] Chen, G.Y. and Craven, B.D. Existence and continuity of solutions for vector optimization, J. Optim. Theory Appl. 81(3) (1994), 459–468.
[9] Chen, G.Y., Huang, X. and Yang, X. Vector Optimization, Set-Valued and Variational Analysis, Springer, Berlin, 2005.
[10] Chen, G.Y. and Yang, X.Q. Characterizations of variable domination structures via nonlinear scalarization, J. Optim. Theory Appl. 112 (2002), 97–110.
[11] Dauer, J.P. and Saleh, O.A. A characterization of proper minimal points as solutions of sublinear optimizations problems, J. Math. Anal. Appl. 178 (1993), 227–246.
[12] Durea, M., Florea E.A. and Strugriu, R. Henig proper efficiency in vector optimization with variable ordering structure, J. Ind. Manag. Optim. 15(2) (2019), 791–815.
[13] Eichfelder, G. Optimal elements in vector optimization with a variable ordering structure, J. Optim. Theory Appl. 151 (2011), 217–240.
[14] Eichfelder, G. Vector optimization in medical engineering, in Pardalos PM, Rassias TM (eds.) Mathematics Without Boundaries Springer, New York, (2014), 181–215.
[15] Eichfelder, G. Variable Ordering Structures in Vector Optimization, Springer, Berlin, 2014.
[16] Eichfelder, G. and Gerlach, T. Characterization of properly optimal el-ements with variable ordering structures, Optimization, 65 (2016), 571–588.
[17] Eichfelder, G., Kasimbeyli, R. Properly optimal elements in vector op-timization with variable ordering structure, J. Global Optim. 60 (2014), 689–712.
[18] Engau, A. Variable preference modeling with ideal-symmetric convex cones, J. Global Optim. 42 (2008), 295–311.
[19] Foroutannia, D. and Mahmodinejad, A. The concept of B-efficient solu-tion in fair multiobjective optimization problems, Iran. J. Numer. Anal. Optim. 7(1) (2017), 47–63.
[20] Geoffrion, A. Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22 (1968), 618–630.
[21] Ghaznavi-Ghosoni, B.A., Khorram E. and Soleimani-Damaneh, M. Scalarization for characterization of approximate strong/weak/proper efficiency in multi-objective optimization, Optimization, 62(6) (2013), 703–720.
[22] Guerraggio, A., Molho, E. and Zaffaroni, A. On the notion of proper efficiency in vector optimization, J. Optim. Theory Appl. 82 (1994), 1–21.
[23] Helbig, S. On a new concept for ε-efficiency, talk at Optimization Days 1992, Montreal, (1992).
[24] Helbig, S. and Pateva, D. On several concepts for ε-efficiency, OR Spec-trum, 16 (1994), 179–186.
[25] Henig, M.I. Proper efficiency with respect to cones, J. Optim. Theory Appl. 36 (1982), 387–407.
[26] Hoseinpour, N. and Ghaznavi, M. Identifying approximate proper effi-ciency in an infinite dimensional space, RARO Operations Research, 57 (2023) 697–714.
[27] Jahn, J. Vector optimization, Springer, Berlin, 2012.
[28] Kiyani, E. and Soleimani-damaneh, M. Approximate proper efficiency on real linear vector spaces, Pacific Journal of Optimization, 10 (2014), 715–734.
[29] Kuhn, H. and Tucker, A. Nonlinear programming, in Neyman, J. (ed.) Proceeding of the Second Berkeley Symposium on Mathematical Statis-tics and Probability, University of California Press, Berkeley, California, (1951) 481–492.
[30] Kutateladze, S.S. convex ε-programming, Soviet. Math. Dokl, 20 (1979), 391–393.
[31] Luc, D.T. and Soubeyran, A. Variable preference relations: existence of maximal elements, J. Math. Econ. 49 (2013), 251–262.
[32] Maghri, E.l. and Pareto-Fenchel, M. ε-subdifferential sum rule and ε-efficiency, Optim. Lett. 6 (2012), 763–781.
[33] N´emeth, A.B. A nonconvex vector minimization problem, Nonlinear Anal. 10 (1986), 669–678.
[34] Rong, W. Proper ε-efficiency in vector optimization problems with cone-subconvexlikeness, Acta Sci. Natur. Univ. NeiMongol, 28 (1997), 609–613.
[35] Shahbeyk, S. and Soleimani-damaneh, M. Proper minimal points of non-convex sets in Banach spaces in terms of the limiting normal cone, Op-timization, 66 (2017), 473–489.
[36] Shahbeyk, S. and Soleimani-damaneh, M. Limiting proper minimal points of nonconvex sets in finite-dimensional spaces, Carpathian J. Math. 35(3) (2019), 370–384.
[37] Shahbeyk, S., Soleimani-damaneh, M. and Kasimbeyli, R. Hartley prop-erly and super nondominated solutions in vector optimization with a variable ordering structure, J. Global Optim. 71 (2018), 383–405.
[38] Soleimani, B. Characterization of Approximate Solutions of Vector Op-timization Problems with a Variable Order Structure, J. Optim. Theory Appl. 162 (2014), 605–632.
[39] Soleimani, B. and Tammer, C. Concepts for approximate solutions of vector optimization problems with variable order structure, Vietnam J. Math. 42 (2014), 43–566.
[40] Tammer, C. Stability results for approximately efficient solutions, OR Spectrum, 16 (1994), 47–52.
[41] Tanaka, T. A new approach to approximation of solutions in vector optimization problems, in Proceeding of APORS, 1994, M. Fushimi and K. Tone, eds., World Scientific Publishing, Singapore, (1995) 497–504.
[42] Wacker, M. and Deinzer, F. Automatic robust medical image registration using a new democratic vector optimization approach with multiple mea-sures, in Yang GZ, Hawkes D, Rueckert D, Noble A, Taylor C, editors. Vol. 5761, Lecture notes in computer science, 12th International Con-ference, MICCAI 2009, 2009 Sept 20–24. Heidelberg, Springer, London, UK, (2009) 590–597.
[43] White, D.J. Epsilon efficiency, J. Optim. Theory Appl. 49 (1986), 319–337.
[44] Yu, P.l. Cone convexity, cone extreme points, and nondominated solu-tions in decision problems with multiobjectives, J. Optim. Theory Appl. 14 (1974), 319–377.
[45] Zamani, M. and Soleimani-damaneh, M. Proper efficiency, scalarization and transformation in multi-objective optimization: unified approaches, Optimization, (2020), 1–22.
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