Journal of Global Optimization

, Volume 55, Issue 1, pp 125–140 | Cite as

Second-order multiobjective symmetric duality involving cone-bonvex functions



In this paper, a new pair of second-order multiobjective symmetric dual programs over arbitrary cones is formulated and appropriate duality theorems are then established under K-η-bonvexity assumptions. We identify a function lying exclusively in the class of K-η-bonvex and not in class of invex function already existing in literature. Self duality is also obtained by assuming the functions involved to be skew-symmetric.


Multiobjective programming Symmetric duality K-η-bonvexity Duality theorems Efficient solutions 


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  1. 1.
    Ahmad I., Husain Z.: On multiobjective second-order symmetric duality with cone constraints. Eur. J. Oper. Res. 204, 402–409 (2010)CrossRefGoogle Scholar
  2. 2.
    Bazaraa M.S., Goode J.J.: On symmetric duality in nonlinear programming. Oper. Res. 21, 1–9 (1973)CrossRefGoogle Scholar
  3. 3.
    Chinchuluun A., Pardalos P.M.: A survey of recent developments in multiobjective optimization. Ann. Oper. Res. 154, 29–50 (2007)CrossRefGoogle Scholar
  4. 4.
    Dantzig G.B., Eisenberg E., Cottle R.W.: Symmetric dual nonlinear programs. Pac. J. Math. 15, 809–812 (1965)CrossRefGoogle Scholar
  5. 5.
    Gulati T.R., Ahmad I., Husain I.: Second-order symmetric duality with generalized convexity. Opsearch 38, 210–222 (2001)Google Scholar
  6. 6.
    Gulati T.R., Mehndiratta G.: Nondifferentiable multiobjective Mond-Weir type second-order symmetric duality over cones. Optim. Lett. 4, 293–309 (2010)CrossRefGoogle Scholar
  7. 7.
    Gulati T.R., Saini H., Gupta S.K.: Second-order multiobjective symmetric duality with cone constraints. Eur. J. Oper. Res. 205, 247–252 (2010)CrossRefGoogle Scholar
  8. 8.
    Kaul R.N., Kaur S.: Optimality criteria in nonlinear programming involving nonconvex functions. J. Math. Anal. Appl. 105, 104–112 (1985)CrossRefGoogle Scholar
  9. 9.
    Khurana S.: Symmetric duality in multiobjective programming involving generalized cone-invex functions. Eur. J. Oper. Res. 165, 592–597 (2005)CrossRefGoogle Scholar
  10. 10.
    Mangasarian O.L.: Second and higher-order duality in nonlinear programming. J. Math. Anal. Appl. 51, 607–620 (1975)CrossRefGoogle Scholar
  11. 11.
    Miettinen K.M.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)Google Scholar
  12. 12.
    Mishra S.K., Lai K.K.: Second-order symmetric duality in multiobjective programming involving generalized cone-invex functions. Eur. J. Oper. Res. 178, 20–26 (2007)CrossRefGoogle Scholar
  13. 13.
    Mond B.: Second-order duality for nonlinear programs. Opsearch 11, 90–99 (1974)Google Scholar
  14. 14.
    Mond B., Hanson M.A.: On duality with generalized convexity. Optimization 15, 313–317 (1984)Google Scholar
  15. 15.
    Mond B., Weir T.: Generalized concavity and duality. In: Schaible, S., Ziemba, W.T. (eds) Generalized Concavity in Optimization and Economics, pp. 263–279. Academic Press, New York (1981)Google Scholar
  16. 16.
    Suneja S.K., Aggarwal S., Davar S.: Multiobjective symmetric duality involving cones. Eur. J. Oper. Res. 141, 471–479 (2002)CrossRefGoogle Scholar
  17. 17.
    Suneja S.K., Lalitha C.S., Khurana S.: Second-order symmetric duality in multiobjective programming. Eur. J. Oper. Res. 144, 492–500 (2003)CrossRefGoogle Scholar
  18. 18.
    Yang X.M., Yang X.Q., Teo K.L., Hou S.H.: Multiobjective second-order symmetric duality with F-convexity. Eur. J. Oper. Res. 165, 585–591 (2005)CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology PatnaPatnaIndia
  2. 2.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia

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