Skip to main content
SpringerLink
Log in

Optimality and duality in vector optimization problems involving arcwise connected d-type-I functions over cones

  • Theoretical Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

In this paper arcwise cone connected d-type-I, quasi cone connected d-type-I, pseudo cone connected d-type-I and other related functions are defined for a vector optimization problem over cones. Sufficient optimality conditions are studied for this problem. Wolfe type, Mond Weir type and mixed type duals are formulated and duality results are established by using the above defined functions.

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. Hanson, M.A.: On sufficiency of the Kuhn Tucker conditions. J. Math. Anal. Appl. 80, 545–550 (1981)

    Article  Google Scholar 

  2. Hanson, M.A., Mond, B.: Necessary and sufficient conditions in constrained optimization. Math. Program. 37(1), 51–58 (1987)

    Article  Google Scholar 

  3. Rueda, N.G., Hanson, M.A.: Optimality criteria in mathematical programming involving generalized invexity. J. Math. Anal. Appl. 130, 375–385 (1988)

    Article  Google Scholar 

  4. Kaul, R.N., Suneja, S.K., Srivastava, M.K.: Optimality criteria and duality in multiple objective optimization involving generalized invexity. J. Optim. Theory Appl. 80(3), 465–482 (1994)

    Article  Google Scholar 

  5. Suneja, S.K., Khurana, S., Bhatia, M.: Optimality and duality in vector optimization involving generalized type I functions over cones. J. Glob. Optim. 49(1), 23–35 (2011)

    Article  Google Scholar 

  6. Aghezzaf, B., Hachimi, M.: Generalized invexity and duality in multiobjective programming problems. J. Glob. Optim. 18(1), 91–101 (2000)

    Article  Google Scholar 

  7. Hachimi, M., Aghezzaf, B.L.: Sufficiency and duality in differentiable multiobjective programming involving generalized type-I functions. J. Math. Anal. Appl. 296(2), 382–392 (2004)

    Article  Google Scholar 

  8. Mishra, S.K., Wang, S.Y., Lai, K.K.: Optimality and duality in nondifferentiable and multiobjective programming under generalized d-invexity. J. Glob. Optim. 29, 425–438 (2004)

    Article  Google Scholar 

  9. Mishra, S.K., Giorgi, G., Wang, S.Y.: Duality in vector optimization in Banach Spaces with generalized convexity. J. Glob. Optim. 29(4), 415–424 (2004)

    Article  Google Scholar 

  10. Mishra, S.K., Wang, S.Y., Lai, K.K.: Multiple objective fractional programing involving semilocally type-I preinvex and related functions. J. Math. Anal. Appl. 310(2), 626–640 (2005)

    Article  Google Scholar 

  11. Ortega, J.M., Rheinboldt, W.C.: Iterative solution of non linear equations in several variables. Academic, New York (1970)

    Google Scholar 

  12. Avriel, M., Zang, I.: Generalized arcwise-connected functions and characterizations of local-global minimum properties. J. Optim. Theory Appl. 32(4), 407–425 (1980)

    Article  Google Scholar 

  13. Singh, C.: Elementary properties of arcwise connected set and functions. J. Optim. Theory Appl. 41(2), 377–387 (1983)

    Article  Google Scholar 

  14. Mukerhjee, R.N., Yadav, S.R.: A note on arcwise connected sets and functions. Bull. Aust. Math. Soc. 31(3), 369–375 (1985)

    Article  Google Scholar 

  15. Bhatia, D., Mehra, A.: Optimality and duality involving arcwise connected and generalized arcwise connected functions. J. Optim. Theory Appl. 100(1), 181–194 (1999)

    Article  Google Scholar 

  16. Yu, G., Wang, M.: Optimality for multi-objective programming involving arcwise connected d-type-I functions. American J. Oper. Res. 1, 243–248 (2011)

    Article  Google Scholar 

  17. Cambini, R., Carosi, L.: Mixed type duality for multiobjective optimization problems with set constraints, in optimality conditions in vector optimization. Manuel Arana Jimenez, Gabreil Ruiz-Garzon and Antonio Rufian-Lizan, eds., Bentham Science Publishers, Bussum, The Netherlands, 119–142 (2010)

  18. Mukherjee, R.N.: Arcwise connected functions and applications in multiobjective optimization. Optimization 39, 151–163 (1997)

    Article  Google Scholar 

  19. Hayashi, M., Komiya, H.: Perfect duality for convexlike programs. J. Optim. Theory Appl. 38(2), 179–189 (1982)

    Article  Google Scholar 

  20. Illes, T., Kassay, G.: Theorem of alternative and optimality conditions for convexlike and general convexlike programming. J. Optim. Theory Appl. 101(2), 243–257 (1999)

    Article  Google Scholar 

Download references

Acknowledgement

The authors are thankful to the anonymous reviewers for their valuable comments and suggestions which has improved the presentation of the paper.

Author information

Authors and Affiliations

  1. Miranda House, Department of Mathematics, University of Delhi, Delhi, 110007, India

    Surjeet Kaur Suneja

  2. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Megha Sharma

Authors
  1. Surjeet Kaur Suneja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Megha Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Megha Sharma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suneja, S.K., Sharma, M. Optimality and duality in vector optimization problems involving arcwise connected d-type-I functions over cones. OPSEARCH 52, 884–902 (2015). https://doi.org/10.1007/s12597-015-0214-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-015-0214-9

Keywords

Mathematics Subject Classification (2000)

Search

Navigation