Characterizing ϵ-properly efficient solutions

References

• M. Beldiman, E. Panaitescu, and L. Dogaru, Approximate quasi efficient solutions in multiobjective optimization, Bull. Math. Soc. Sci. Math. Roumanie Tome. 99 (2008), pp. 109–121.
   Google Scholar
• S. Deng, On approximate solutions in convex vector optimization, SIAM J. Control Optim. 35 (1997), pp. 2128–2136. doi: 10.1137/S0363012995292561
   Web of Science ®Google Scholar
• J. Dutta and V. Vetrivel, On approximate minima in vector optimization, Numer. Funct. Anal. Optim. 22 (2001), pp. 845–859. doi: 10.1081/NFA-100108312
   Web of Science ®Google Scholar
• A. Engau and M.M. Wiecek, Cone characterizations of approximate solutions in real vector optimization, J. Optim. Theory Appl. 134 (2007), pp. 499–513. doi: 10.1007/s10957-007-9235-8
   Web of Science ®Google Scholar
• A. Engau and M.M. Wiecek, Generating epsilon-efficient solutions in multi-objective programming, Eur. J. Oper. Res. 177 (2007), pp. 1566–1579. doi: 10.1016/j.ejor.2005.10.023
   Web of Science ®Google Scholar
• F. Flores-Bazán and E. Hernández, A unified vector optimization problem: complete scalarizations and applications, Optimization. 60(12) (2011), pp. 1399–1419.
   Google Scholar
• Y. Gao, X. Yang, and H.W.J. Lee, Optimality conditions for approximate solutions in multiobjective optimization problems, J. Inequal. Appl. (2010), Article No. 620928.
   Google Scholar
• Y. Gao, X. Yang, and K.L. Teo, Optimality conditions for approximate solutions in vector optimization problems, J. Ind. Manag. Optim. 7 (2011), pp. 483–496. doi: 10.3934/jimo.2011.7.483
   Web of Science ®Google Scholar
• B.A. Ghaznavi-ghosoni and E. Khorram, On approximating weakly/properly efficient solutions in multi-objective programming, Math. Comput. Model. 54 (2011), pp. 3172–3181. doi: 10.1016/j.mcm.2011.08.013
   Web of Science ®Google Scholar
• B.A. Ghaznavi-ghosoni, E. Khorram, and M. Soleimani-damaneh, Scalarization for characterization of approximate strong/weak/proper efficiency in multi-objective optimization, Optimization. 62(6) (2013), pp. 703–720. doi: 10.1080/02331934.2012.668190
   Web of Science ®Google Scholar
• C. Gutierrez, B. Jimenez, and V. Novo, A unified approach and optimality conditions for approximate solutions of vector optimization problems, SIAM J. Optim. 17 (2006), pp. 688–710. doi: 10.1137/05062648X
   Web of Science ®Google Scholar
• C. Gutierrez, B. Jimenez, and V. Novo, On approximate solutions in vector optimization problems via scalarization, Comput. Optim. Appl. 35 (2006), pp. 305–324. doi: 10.1007/s10589-006-8718-0
   Web of Science ®Google Scholar
• C. Gutierrez, B. Jimenez, and V. Novo, Optimality conditions for metrically consistent approximate solutions in vector optimization, J. Optim. Theory Appl. 133 (2007), pp. 49–64. doi: 10.1007/s10957-007-9191-3
   Web of Science ®Google Scholar
• C. Gutierrez, B. Jimenez, and V. Novo, Optimality conditions via scalarization for a new ϵ-efficiency concept in vector optimization problems, Eur. J. Oper. Res. 201 (2010), pp. 11–22. doi: 10.1016/j.ejor.2009.02.007
   Web of Science ®Google Scholar
• S. Helbig and D. Pateva, On several concepts for ϵ-efficiency, OR Spect. 16 (1994), pp. 179–186.
   Google Scholar
• J.H. Jia and Z.F. Li, ϵ-Conjugate maps and ϵ-conjugate duality in vector optimization with set-valued maps, Optimization 57 (2008), pp. 621–633. doi: 10.1080/02331930802355374
   Web of Science ®Google Scholar
• S.S. Kutateladze, Convex ϵ-programming, Sov. Math. Dokl. 20 (1979), pp. 391–393.
   Google Scholar
• Z. Li, ϵ-Optimality and ϵ-duality of nonsmooth nonconvex multiobjective programming, J. Univ. Inner Mongolia 25 (1994), pp. 599–608.
   Google Scholar
• Z. Li and S. Wang, ϵ-Approximation solutions in multiobjective optimization, Optimization 44 (1998), pp. 161–174. doi: 10.1080/02331939808844406
   Google Scholar
• J.C. Liu, ϵ-Properly efficient solutions to nondifferentiable multi-objective programming problems, Appl. Math. Lett. 12 (1999), pp. 109–113. doi: 10.1016/S0893-9659(99)00087-7
   Web of Science ®Google Scholar
• J.C. Liu, ϵ-Duality theorem of nondifferentiable nonconvex multiobjective programming, J. Optim. Theory Appl. 69 (1991), pp. 153–167. doi: 10.1007/BF00940466
   Web of Science ®Google Scholar
• P. Loridan, Necessary conditions for ϵ-optimality, Math. Prog. Study. 19 (1982), pp. 140–152. doi: 10.1007/BFb0120986
   Web of Science ®Google Scholar
• P. Loridan, ϵ-Solutions in vector minimization problems, J. Optim. Theory Appl. 43 (1984), pp. 265–276. doi: 10.1007/BF00936165
   Web of Science ®Google Scholar
• P. Loridan, ϵ-Duality theorem of nondifferentiable nonconvex multiobjective programming, J. Optim. Theory Appl. 74 (1992), pp. 565–566. doi: 10.1007/BF00940327
   Web of Science ®Google Scholar
• A.B. Nemeth, Between Pareto efficiency and Pareto ϵ-efficiency, Optimization 20 (1989), pp. 615–637. doi: 10.1080/02331938908843483
   Google Scholar
• A. Pascoletti and P. Serafini, Scalarizing vector optimization problems, J. Optim. Theory Appl. 42 (1984), pp. 499–524. doi: 10.1007/BF00934564
   Web of Science ®Google Scholar
• T.Q. Son, J.J. Strodiot, and V.H. Nguyen, ϵ-Optimality and ϵ-Lagrangian duality for a nonconvex programming problem with an infinite number of constraints, J. Optim. Theory Appl. 141 (2009), pp. 389–409. doi: 10.1007/s10957-008-9475-2
   Web of Science ®Google Scholar
• T. Tanaka, A new approach to approximation of solutions in vector optimization problems, in Proceedings of APORS 1994, M. Fushimi and K. Tone, eds., World Scientific Publishing, Singapore, 1995, pp. 479–504.
   Google Scholar
• T. Tanaka, Approximately efficient solutions in vector optimization, J. Multi-Criteria Decis. Anal. 5 (1996), pp. 271–278. doi: 10.1002/(SICI)1099-1360(199612)5:4<271::AID-MCDA114>3.0.CO;2-W
   Google Scholar
• I. Valyi, Approximate solutions of vector optimization problems, in Systems Analysis and Simulation, A. Sydow, M. Thoma, and R. Vichnevetsky, eds., Akademie-Verlag, Berlin, 1985, pp. 246–250.
   Google Scholar
• D.J. White, Epsilon efficiency, J. Optim. Theory Appl. 49 (1986), pp. 319–337. doi: 10.1007/BF00940762
   Web of Science ®Google Scholar
• K. Yokoyama, Epsilon approximate solutions for multi-objective programming problems, J. Math. Anal. Appl. 203 (1996), pp. 142–149. doi: 10.1006/jmaa.1996.0371
   Web of Science ®Google Scholar