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Sufficient efficiency criteria in multiobjective fractional programming with generalized \(\left( \mathcal {F},b,\phi ,\rho ,\theta \right) \)-univex \(n\)-set functions

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Abstract

We consider some types of generalized convexity and discuss new global semiparametric sufficient efficiency conditions for a multiobjective fractional programming problem involving \(n\)-set functions.

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References

  1. Corley, H.W.: Optimization theory for \(n\)-set functions. J. Math. Anal. Appl. 127(1), 193–205 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  2. Mishra, S.K.: Duality for multiple objective fractional subset programming with generalized (\({\cal F}, \rho, \sigma, \theta \))-V-type-I functions. J. Glob. Optim. 36(4), 499–516 (2006)

    Article  Google Scholar 

  3. Mishra, S.K., Jaiswal, M., Pankaj.: Optimality conditions for multiple objective fractional subset programming with \(\left(\rho , \sigma , \theta \right)\)-type-I and related non-convex functions. Calcolo 49(3), 177–192 (2012)

  4. Mishra, S.K., Wang, S.Y., Lai, K.K.: Optimality and duality for a multi-objective programming problem involving generalized d-type-I and related n-set functions. Eur. J. Oper. Res. 173(2), 405–418 (2006)

  5. Mishra, S.K., Wang, S.Y., Lai, K.K.: Optimality conditions for multiple objective fractional subset programming with \(\left({\cal F}, \rho, \sigma, \theta \right)\)-V-type I and related non-convex functions. Math. Comput. Model. 48(7–8), 1201–1212 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mishra, S.K., Wang, S.Y., Lai, K.K.: Generalized Convexity and Vector Optimization. Nonconvex Optimization and Its Applications, vol. 90. Springer, Berlin (2009)

  7. Morris, R.J.T.: Optimal constrained selection of a measurable subset. J. Math. Anal. Appl. 70(2), 546–562 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Stancu-Minasian, I.M., Paraschiv, A.: Global semiparametric sufficient efficiency conditions in multiobjective fractional programming with generalized \(\left( {\cal {F}}, b,\phi,\rho,\theta \right) \)-univex \(n\)-set functions. Rev. Roumaine Math. Pures Appl. 54(4), 331–345 (2009)

    MathSciNet  MATH  Google Scholar 

  9. Stancu-Minasian, I.M., Preda, V.: Optimality conditions and duality for programming problems involving set and \(n\)- set functions: a survey. J. Stat. Manag. Syst. 5(1–3), 175–207 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Stancu-Minasian, I.M., Stancu, A.M.: New global semiparametric sufficient efficiency conditions in multiobjective fractional programming with generalized \(\left({\cal {F}}, b,\phi ,\rho ,\theta \right) \)-univex \(n\)-set functions. J. Stat. Manag. Syst. (accepted)

  11. Zalmai, G.J.: Generalized \(\left({\cal {F}}, b,\phi ,\rho ,\theta \right)\) -univex \(n\)-set functions and global semiparametric sufficient efficiency conditions in multiobjective fractional subset programming. Int. J. Math. Math. Sci. No. 6, 949–973 (2005)

  12. Zalmai, G.J.: Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized \(( {\cal {F}},\alpha,\rho,\theta )\)-\(V\)-convex functions. Comput. Math. Appl. 43(12), 1489–1520 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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Stancu, A.M., Stancu-Minasian, I.M. Sufficient efficiency criteria in multiobjective fractional programming with generalized \(\left( \mathcal {F},b,\phi ,\rho ,\theta \right) \)-univex \(n\)-set functions. Optim Lett 11, 1029–1045 (2017). https://doi.org/10.1007/s11590-014-0783-1

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