Skip to main content
SpringerLink
Log in

Duality for Multiple Objective Fractional Programming with Generalized Type-I Univexity

  • Conference paper
  • First Online:
Book cover Optimization Theory, Decision Making, and Operations Research Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 31))

Abstract

In this paper, a multiobjective fractional subset programming problem (Problem (P)) is considered. A new class of \(\left(\mathcal{F},b,\phi,\rho,\theta \right)\) -type-I univex function is introduced and a general dual model for (P) is presented. Based on these functions, weak, strong and converse duality theorems are derived. Almost all results presented in the literature were obtained under the assumption that the function ℱ is sublinear in the third argument. Here, our results hold assuming only the convexity of this one.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bătătorescu, A., Preda, V., Beldiman, M.: On higher order duality for multiobjective programming involving generalized \(\left(\mathcal{F},\rho,\gamma,b\right)\) -convexity. Math. Rep. 9(59), 161–174 (2007)

    Google Scholar 

  2. Bector, C.R., Bhatia, D., Pandey, S.: Duality for multiobjective fractional programming involving n-set functions. J. Math. Anal. Appl. 186(3), 747–768 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chinchuluun, A., Yuan, D., Pardalos, P.M.: Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity. Ann. Oper. Res. 154(1), 133–147 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Lee, T.Y.: Generalized convex set functions. J. Math. Anal. Appl. 141(1), 278–290 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lin, L.J.: On the optimality of differentiable nonconvex n-set functions. J. Math. Anal. Appl. 168(2), 351–366 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. 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 

  9. Preda, V.: On minmax programming problems containing n-set functions. Optimization 22(4), 527–537 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Preda, V.: On efficiency and duality for multiobjective programms. J. Math. Anal. Appl. 166(2), 365–377 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Preda, V.: On duality of multiobjective fractional measurable subset selection problems, J. Math. Anal. Appl. 196(2), 514–525 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. Preda, V., Stancu-Minasian, I.M., Beldiman, M., Stancu, A.: Optimality and duality for multiobjective programming with generalized V-type I univexity and related n-set functions. Proc. Rom. Acad. Ser. A 6(3), 183–191 (2005)

    MathSciNet  MATH  Google Scholar 

  13. Preda, V., Stancu-Minasian, I.M., Beldiman, M., Stancu, A.: Generalized V-univexity type-I for multiobjective programming problems with n-set function. J. Global Optim. 44(1), 131–148 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Stancu-Minasian, I.M., A sixth bibliography of fractional programming. Optimization 55(4), 405–428 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. 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)

    MathSciNet  MATH  Google Scholar 

  16. Yuan, D.H., Liu, X.L., Chinchuluun, A., Pardalos, P.M., Nondiferentiable minimax fractional programming problems with (C; α ; ρ; d)-convexity. J. Optim. Theor. Appl. 129(1), 185–199 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Zalmai, G.J.: Generalized \(\left(\mathcal{F},b,\phi,\rho,\theta \right)\) -univex n-set functions and global semiparametric sufficient efficiency conditions in multiobjective fractional subset programming. Int. J. Math. Math. Sci. 6, 949–973 (2005)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematical Statistics and Applied Mathematics, of the Romanian Academy, Calea 13 Septembrie Nr. 13, Sector 5, Bucharest, Romania

    Ioan M. Stancu-Minasian & Andreea Mădălina Stancu

Authors
  1. Ioan M. Stancu-Minasian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreea Mădălina Stancu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreea Mădălina Stancu .

Editor information

Editors and Affiliations

  1. , Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Athanasios Migdalas

  2. , Economical and Social Sciences, University of Macedonia, Loggou-Tourpali, Naoussa, 59200, Greece

    Angelo Sifaleras

  3. , Department of Applied Informatics, University of Macedonia, Egnatia St. 156, Thessaloniki, 54006, Greece

    Christos K. Georgiadis

  4. , Department of Marketing and Operations M, University of Macedonia, Agiou Dimitriou 49, Edessa, 58200, Greece

    Jason Papathanasiou

  5. , Department of Applied Informatics, University of Macedonia, Egnatia Street 156, Thessaloniki, 54006, Greece

    Emmanuil Stiakakis

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this paper

Cite this paper

Stancu-Minasian, I.M., Stancu, A.M. (2013). Duality for Multiple Objective Fractional Programming with Generalized Type-I Univexity. In: Migdalas, A., Sifaleras, A., Georgiadis, C., Papathanasiou, J., Stiakakis, E. (eds) Optimization Theory, Decision Making, and Operations Research Applications. Springer Proceedings in Mathematics & Statistics, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5134-1_14

Download citation

Publish with us

Policies and ethics

Search

Navigation