Skip to main content
Log in

On Sufficiency and Duration in Nonsmooth Multiobjective Programming

  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

A nonsmooth multiobjective programming problem is considered and Kuhn-Tucker type sufficient conditions are derived for properly efficiency solutions. Weak and strong duality results are established for Mon-Weir type dual. These results are obtained under generalized convexity assumptions.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R.H. CLARKE, “Optimization and nonsmooth analysis”, Wiley-lnterscience, New York 1983.

    Google Scholar 

  2. B.D. CRAVEN, “Invex functions and constrained locak minima”, Bull. Austral. Math. Soc. 24 (1981), 357–366.

    Article  Google Scholar 

  3. R.R. Egudo AND M.A. HANSON, “On sufficiency of Kuhn-tucker conditions in nonsmooth multiobjective programming”, FSU Technical Report Number M-888, 1993.

    Google Scholar 

  4. R.R. EGUDO, T. WEIR AND O. MOND, “Duality without constraint qualification for multiobjective programming”, J. Austral. Math. Soc. Series B 33 (1992), 531–544.

    Article  Google Scholar 

  5. A.M. GEOFFRION, “Proper efficiency and the theory of vector maximization”, J. Math. Anal, Appl., 22 (1968), 618–630.

    Article  Google Scholar 

  6. T.R. GULATI AND N. TALLT, “Sufficiency and duality in non-differentiable multiobjective programming:, Opsearch 28 (1991), 73–87.

    Google Scholar 

  7. M.A. HANSON AND B. MOND, “Necessary and sufficient conditions in constrained optimization, Math, Prog. 37 (1987), 51–58.

    Article  Google Scholar 

  8. V. JEYAKUMAR, “Strong and Weak invexity in mathematical programming,” Methods Oper. Res 55 (1985), 109–125.

    Google Scholar 

  9. V. JEYAKUMAR AND B. Mond, “On generalized convex mathematical programming”, J. Austral. Math. Soc. Series B 39 (1992), 43–53.

    Article  Google Scholar 

  10. R. KANNIAPPAAN AND S.M.A. Sastry, “Duality theorems and an optimality condition for nondifferentiable convex programming”, J. Austral. Math. Soc. Series A 32 (1988) 369–379.

    Article  Google Scholar 

  11. H.C. LAI AND C.P. HO, “Duality theorem of non-differentiable convex multiobjective programming:, J. Optim. Theory Appl. 50 (1986), 407–420.

    Article  Google Scholar 

  12. S.K. MISHRA AND R.N. Mukherjee. “On generalized convex multiobjective non-smooth programming”, J. Austral. Math. Soc, Ser B. 38 (1996), 140–148.

    Article  Google Scholar 

  13. F. ZHAO, “On sufficiency of the Kuhn-Tucker conditions in non-differentiable program-ming”, Bull. Austral. Math. Soc. 46 (1992), 385–389.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishra, S.K. On Sufficiency and Duration in Nonsmooth Multiobjective Programming. OPSEARCH 34, 221–231 (1997). https://doi.org/10.1007/BF03398527

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03398527

Navigation