Skip to main content

Advertisement

SpringerLink
Log in

Optimality and duality for nonsmooth multiobjective fractional programming with mixed constraints

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

Abstract

We consider nonsmooth multiobjective fractional programming problems with inequality and equality constraints. We establish the necessary and sufficient optimality conditions under various generalized invexity assumptions. In addition, we formulate a mixed dual problem corresponding to primal problem, and discuss weak, strong and strict converse duality theorems.

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. Aghezzaf B. and Hachimi M. (2001). Sufficiency and duality in multiobjective programming involving generalized (F, ρ)-convexity. J. Math. Anal. Appl. 258: 617–628

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Bector C.R., Chandra S. and Husain I. (1993). Optimality condition and duality in subdifferentiable multiobjective fractional programming. J. Optim. Theory Appl. 79(1): 105–125

    Article  Google Scholar 

  4. Chen X. (2002). Optimality and duality for the multiobjective fractional programming with the generalized (F, ρ) convexity. J. Math. Anal. Appl. 273: 190–205

    Article  Google Scholar 

  5. Chew K.L. and Choo E.U. (1984). Pseudolinearity and efficiency. Math. Program. 28: 226–239

    Article  Google Scholar 

  6. Clarke, F.H., Ledyaev, Ledyaer, Y.S., Stern, R.J., Wolenski, P.R.: Nonsmooth analysis and control theory. Springer, Graduate Texts in Mathematics, New York (1998)

  7. Clarke F.H. (1983). Optimization and nonsmooth analysis. Wiley-Interscience, New York

    Google Scholar 

  8. Craven B.D. (1986). Nondifferentiable optimization by nonsmooth approximations. Optimization 17: 3–17

    Article  Google Scholar 

  9. Geoffrion A.M. (1968). Proper efficiency and theory of vector maximization. J. Math. Anal. Appl. 22: 618–630

    Article  Google Scholar 

  10. Liang Z.A., Huang H.X. and Pardalos P.M. (2003). Efficiency conditions and duality for a class of multiobjective fractional programming problems. J. Glob. Optim. 27: 447–471

    Article  Google Scholar 

  11. Liu J.C. (1996). Optimality and duality for multiobjective fractional programming involving nonsmooth pseudoinvex functions, (f, ρ)-convex functions. Optim., 36: 333–346

    Article  Google Scholar 

  12. Liu J.C. (1996). Optimality and duality for multiobjective fractional programming involving nonsmooth pseudoinvex functions. Optimization 37: 27–39

    Article  Google Scholar 

  13. Luc D.T. (2002). A multiplier rule for multiobjective programming problems with continuous data. SIAM J. Optim. 13: 168–178

    Article  Google Scholar 

  14. Jourani and A. (1994). Constraint qulalification and Lagrange multipliers in nondifferentiable programming problems. J. Optim. Theory Appl. 81(3): 533–548

    Article  Google Scholar 

  15. Kim D.S. and Schaible S. (2004). Optimality and duality for invex nonsmooth multiobjective programming problems. Optimization 53(2): 165–176

    Article  Google Scholar 

  16. Kuk H. and Tanino T. (2001). Optimality and duality for nonsmooth multiobjective fractional programming with generalized invexity. J. Math. Anal. Appl. 262: 365–375

    Article  Google Scholar 

  17. Mishra S.K., Wang S.Y. and Lai K.K. (2005). Nondifferentiable multiobjective programming under generalized d-invexity. Eur. J. Oper. Res. 160: 218–222

    Article  Google Scholar 

  18. Mukherjee R.N. and Rao C.P. (2000). Mixed type duality for multiobjective variational problem. J. Math. Anal. Appl. 252: 571–586

    Article  Google Scholar 

  19. Nobakhtian S. (2006). Infine functions and nonsmooth multiobjective optimization problems. Comput. Math. Appl. 51: 1385–1394

    Article  Google Scholar 

  20. Nobakhtian S. (2006). Optimality criteria and duality in multiobjective programming involving nonsmooth invex functions. J. Glob. Optim. 35: 593–606

    Article  Google Scholar 

  21. Reiland T.W. (1990). Nonsmooth invexity. Bull. Aust. Math. Soc. 42: 437–446

    Google Scholar 

  22. Sach P.H., Lee G.M. and Kim D.S. (2003). Infine functions, nonsmooth alternative theorems and vector optimization problems. J. Glob. Optim. 27: 51–81

    Article  Google Scholar 

  23. Phuong T.D., Sach P.H. and Yen N.D. (1995). Strict lower semicontinuity of the level sets and invexity of a locally Lipschitz function. J. Optim. Theory. Appl. 87: 579–594

    Article  Google Scholar 

  24. Wolfe P. (1961). A duality theorem for nonlinear programming. Q. Appl. Math. 19: 239–244

    Google Scholar 

  25. Weir T. and Mond B. (1989). Generalized convexity and duality in multiobjective programming. Bull. Aust. Math. Soc. 39: 287–299

    Google Scholar 

  26. Zhang Z. and Mond B. (1997). Duality for a nondifferentiable programming problem. Bull. Aust. Math. Soc. 55: 29–44

    Article  Google Scholar 

  27. Xu Z. (1996). Mixed type duality in multiobjective programming problems. J. Math. Anal. Appl. 198: 621–635

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran

    S. Nobakhtian

Authors
  1. S. Nobakhtian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Nobakhtian.

Additional information

This research was partially supported by Project no. 850203 and Center of Excellence for Mathematics, University of Isfahan, Iran.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nobakhtian, S. Optimality and duality for nonsmooth multiobjective fractional programming with mixed constraints. J Glob Optim 41, 103–115 (2008). https://doi.org/10.1007/s10898-007-9168-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-007-9168-7

Keywords

2000 Mathematics Subject Classification

Search

Navigation