On a practical notion of Geoffrion proper optimality in multicriteria optimization

References

• Luc DT. Theory of vector optimization. Vol. 319 of Lecture Notes in Economics and Mathematical Systems. Berlin: Springer-Verlag; 1989.
   Google Scholar
• Miettinen K. Nonlinear multicriteria optimization. International Series in Operations Research & Management Science, 12. Boston (MA): Kluwer Academic Publishers; 1999.
   Google Scholar
• Ehrgott M. Multicriteria optimization. 2nd ed. Berlin: Springer-Verlag; 2005.
   Google Scholar
• Jahn J. Vector optimization. Berlin: Springer; 2009.
   Google Scholar
• Eichfelder G. Adaptive scalarization methods in multiobjective optimization. Vector optimization. Berlin: Springer-Verlag; 2008.
   Google Scholar
• Kuhn HW, Tucker AW. Nonlinear programming. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950. Berkeley: University of California Press; 1951. p. 481–492.
   Google Scholar
• Geoffrion AM. Proper efficiency and the theory of vector maximization. J Math Anal Appl. 1968;22:618–630. doi: 10.1016/0022-247X(68)90201-1
   Web of Science ®Google Scholar
• Benson HP. Existence of efficient solutions for vector maximization problems. J Optim Theory Appl. 1978;26(4):569–580. doi: 10.1007/BF00933152
   Web of Science ®Google Scholar
• Benson HP. An improved definition of proper efficiency for vector maximization with respect to cones. J Math Anal Appl. 1979;71(1):232–241. doi: 10.1016/0022-247X(79)90226-9
   Web of Science ®Google Scholar
• Henig MI. Proper efficiency with respect to cones. J Optim Theory Appl. 1982;36(3):387–407. doi: 10.1007/BF00934353
   Web of Science ®Google Scholar
• Borwein J. Proper efficient points for maximizations with respect to cones. SIAM J Control Optim. 1977;15(1):57–63. doi: 10.1137/0315004
   Web of Science ®Google Scholar
• Borwein JM, Zhuang D. Super efficiency in vector optimization. Trans Amer Math Soc. 1993;338(1):105–122. doi: 10.1090/S0002-9947-1993-1098432-5
   Web of Science ®Google Scholar
• Ginchev I, Guerraggio A, Rocca M. Geoffrion type characterization of higher-order properly efficient points in vector optimization. J Math Anal Appl. 2007;328(2):780–788. doi: 10.1016/j.jmaa.2006.06.001
   Web of Science ®Google Scholar
• Engau A. Definition and characterization of Geoffrion proper efficiency for real vector optimization with infinitely many criteria. J Optim Theory Appl. 2015;165(2):439–457. doi: 10.1007/s10957-014-0608-5
   Web of Science ®Google Scholar
• Dutta J, Vetrivel V. On approximate minima in vector optimization. Numer Funct Anal Optim. 2001;22(7-8):845–859. doi: 10.1081/NFA-100108312
   Web of Science ®Google Scholar
• Kazmi KR. Existence of ε-minima for vector optimization problems. J Optim Theory Appl. 2001;109(3):667–674. doi: 10.1023/A:1017576007648
   Web of Science ®Google Scholar
• Makarov EK, Rachkovski NN. Unified representation of proper efficiency by means of dilating cones. J Optim Theory Appl. 1999;101(1):141–165. doi: 10.1023/A:1021775112119
   Web of Science ®Google Scholar
• Liu JC. ε-Properly efficient solutions to nondifferentiable multiobjective programming problems. Appl Math Lett. 1999;12(6):109–113. doi: 10.1016/S0893-9659(99)00087-7
   Web of Science ®Google Scholar
• Shukla PK, Dutta J, Deb K. On properly Pareto optimal solutions. Practical Approaches to Multi-Objective Optimization, Dagstuhl Seminar Proceedings 04461, Daghstuhl, Germany. 2005.
   Google Scholar
• Wiecek MM. Advances in cone-based preference modeling for decision making with multiple criteria. Decis Mak Manuf Serv. 2007;1(1-2):153–173.
   Google Scholar
• Hunt BJ, Wiecek MM, Hughes CS. Relative importance of criteria in multiobjective programming: a cone-based approach. Eur J Oper Res. 2010;207(2):936–945. doi: 10.1016/j.ejor.2010.06.008
   Web of Science ®Google Scholar
• Sawaragi Y, Nakayama H, Tanino T. Theory of multiobjective optimization. Vol. 176 of Mathematics in Science and Engineering. Orlando (FL) : Academic Press, Inc.; 1985.
   Google Scholar
• Tanaka T. Approximately efficient solutions for vector optimization problems. Sūrikaisekikenkyūsho Kōkyūroku. 1995;899:159–166; Optimization theory and its applications in mathematical systems, Kyoto, 1994.
   Google Scholar
• Deb K. Multi-objective optimization using evolutionary algorithms. Chichester: Wiley; 2009.
   Google Scholar
• Shukla PK, Hirsch C, Schmeck H. A framework for incorporating trade-off information using multi-objective evolutionary algorithms. Proceedings of the 11th International Conference on Parallel Problem Solving from Nature: Part II; Krakow, Poland; PPSN'10. Berlin: Springer-Verlag; 2010. p. 131–140.
   Google Scholar
• Helbig S, Pateva D. On several concepts for ε-efficiency. Oper Res Spektrum. 1994;16(3):179–186. doi: 10.1007/BF01720705
   Google Scholar
• Guddat J, Guerra Vasquez F, Tammer K, et al. Multiobjective and stochastic optimization based on parametric optimization. Vol. 26 of Mathematical Research. Berlin: Akademie-Verlag; 1985.
   Google Scholar
• Soleimani-damaneh M, Zamani M. On Benson's scalarization in multiobjective optimization. Optim Lett. 2016;10(8):1757–1762. doi: 10.1007/s11590-016-0999-3
   Web of Science ®Google Scholar
• Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput. 2002;6(2):182–197. doi: 10.1109/4235.996017
   Web of Science ®Google Scholar
• Rockafellar RT, Wets RJB. Variational analysis. Berlin: Springer; 1997.
   Google Scholar