Skip to main content
SpringerLink
Log in

Sufficiency and Duality in Multiobjective Variational Problems with Generalized Type I Functions

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

Recently Hachimi and Aghezzaf introduced the notion of (F,α,ρ,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. Here, we extend the concepts of (F,α,ρ,d)-type I and generalized (F,α,ρ, d)-type I functions to the continuous case and we use these concepts to establish various sufficient optimality conditions and mixed duality results for multiobjective variational problems. Our results apparently generalize a fairly large number of sufficient optimality conditions and duality results previously obtained for multiobjective variational problems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Aghezzaf M. Hachimi (2000) ArticleTitleGeneralized invexity and duality in multiobjective programming problems Journal of Global Optimization 18 91–101 Occurrence Handle10.1023/A:1008321026317

    Article  Google Scholar 

  2. B. Aghezzaf M. Hachimi (2001) ArticleTitleSufficiency and duality in multiobjective programming Involving Generalized (F, ρ)-convexity Journal of Mathematical Analysis and Application 258 617–628

    Google Scholar 

  3. Aghezzaf, B. and Khazafi, K. (2002). Generalized B-invexity and duality in multiobjective variational programming problems, Proceedings of the Fourth International Conference on Applied Mathematics and Engineering Sciences, CIMASI, 23–25 october, Casablanca, Morocco.

  4. C.R. Bector I. Husain (1992) ArticleTitleDuality for multiobjective variational problems Journal of mathenmatical Analysis and Application 166 214–229

    Google Scholar 

  5. D. Bhatia A. Mehra (1999) ArticleTitleOptimality conditions and duality for multiobjective variational problems with generalized B-invexity Journal of mathenmatical Analysis and Application 234 341–360

    Google Scholar 

  6. D. Bhatia P. Kumar (1996) ArticleTitleDuality for multiobjective variational problems with B-vex functions optimization 36 347–360

    Google Scholar 

  7. C.R. Bector S. Chandra Abha (2001) ArticleTitleOn mixed duality in mathematical progrmming Journal of mathenmatical Analysis and Application 259 346–356

    Google Scholar 

  8. R. Egudo (1989) ArticleTitleEfficiency and generalized convex duality for multiobjective programs Journal of mathenmatical Analysis and Application 138 84–94

    Google Scholar 

  9. T.R. Gulati M.A. Islam (1994) ArticleTitleSufficiency and duality in multiobjective programming involving generalized F-convex functions Journal of mathenmatical Analysis and Application 183 181–195

    Google Scholar 

  10. M. Hachimi B. Aghezzaf (2004) ArticleTitleSufficiency and duality in differentiable multiobjective programming involving generalized type I functions Journal of Mathematical Analysis and Application 296 382–392

    Google Scholar 

  11. M.A. Hanson (1981) ArticleTitleOn Sufficiency of the Kuhn-Tucker conditions Journal of Mathematical Analysis and Application 80 545–550

    Google Scholar 

  12. M.A. Hanson B. Mond (1982) ArticleTitleFurther generalizations of convexity in mathematical programming Journal of Information Optimization Science 3 25–32

    Google Scholar 

  13. R.N. Kaul S.K. Suneja M.K. Srivastava (1994) ArticleTitleOptimality criteria and duality in multiobjective optimization involving generalized invexity Journal of Optimization Theory and Application 80 465–482

    Google Scholar 

  14. J. C. Liu C.S. Wu (1998) ArticleTitleOn minimax fractional optimality conditions with (F, ρ)-convexity Journal of Mathematical Analysis and Application 219 36–51

    Google Scholar 

  15. T. Maeda (1994) ArticleTitleConstraint qualification in multiobjective optimization problems : Differentiable case Jornal of Optimization Theory Application 80 483–500

    Google Scholar 

  16. B. Mond M.A. Hanson (1967) ArticleTitleDuality for variational problems Journal of Mathematical Analysis and Application 18 355–364

    Google Scholar 

  17. B. Mond S. Chandra I. Husain (1988) ArticleTitleDuality for variational problems with invexity Journal of Mathematical Analysis and Application 134 322–328

    Google Scholar 

  18. S.K. Mishra R.N. Mukherjee (1994) ArticleTitleOn efficiency and duality for multiobjective variational problems Journal of Mathematical Analysis and Application 187 40–54

    Google Scholar 

  19. R.N. Mukherjee Ch. Purnachandra Rao (2000) ArticleTitleMixed type duality for multiobjective variational problems Journal of Mathematical Analysis and Application 252 571–586

    Google Scholar 

  20. C. Nahak C. Nanda (1996) ArticleTitleDuality for multiobjective variational problems with invexity Optimization 36 235–248

    Google Scholar 

  21. V. Preda (1992) ArticleTitleOn Sufficiency and duality for multiobjective program Journal of Mathematical Analysis and Application 166 365–377

    Google Scholar 

  22. N.G. Rueda M.A. Hanson (1988) ArticleTitleOptimality criteria in mathematical programming involving generalized invexity Journal of Mathematical Analysis and Application 130 375–385

    Google Scholar 

  23. T. Weir B. Mond (1989) ArticleTitleGeneralized convexity and duality in multiple objective programming Bulletin of the Australian Mathematical Society 39 287–299

    Google Scholar 

  24. Z. Xu (1996) ArticleTitleMixed type duality in multiobjective programming problems Journal of Mathematical Analysis and Application 198 621–635

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculté des Sciences Juriduques Economiques et Sociales, Université Ibn Zohr, B.P. 8658, Hay Dakhla, Agadir, 80 000, Morocco

    Mohamed Hachimi

  2. Département de Mathématiques et d’Informatique Faculté des Sciences, Université Hassan, II-Aïn chock, B.P. 5366, Maârif Casablanca, Morocco

    Brahim Aghezzaf

Authors
  1. Mohamed Hachimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brahim Aghezzaf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Hachimi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hachimi, M., Aghezzaf, B. Sufficiency and Duality in Multiobjective Variational Problems with Generalized Type I Functions. J Glob Optim 34, 191–218 (2006). https://doi.org/10.1007/s10898-005-1653-2

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-005-1653-2

Keywords

Search

Navigation