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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Peng, Zai Yun Zhao, Yong Yu, Kai Zhi and Lin, Zhi 2014. Semi-G-Preinvexity and Optimality in Mathematical Programming. Journal of Applied Mathematics, Vol. 2014, p. 1.


    Yuan, Dehui and Liu, Xiaoling 2013. G-semipreinvexity and its applications. Arabian Journal of Mathematics, Vol. 2, Issue. 3, p. 321.


    Liu, Xue Wen Zhao, Ke Quan and Chen, Zhe 2012. A Class ofG-Semipreinvex Functions and Optimality. Journal of Applied Mathematics, Vol. 2012, p. 1.


    Zhao, Ke Quan Liu, Xue Wen and Chen, Zhe 2011. A class of r-semipreinvex functions and optimality in nonlinear programming. Journal of Global Optimization, Vol. 49, Issue. 1, p. 37.


    Long, X. J. and Peng, J. W. 2006. Semi-B-Preinvex Functions. Journal of Optimization Theory and Applications, Vol. 131, Issue. 2, p. 301.


    Peng, Jianwen and Long, Xianjun 2004. A remark on preinvex functions. Bulletin of the Australian Mathematical Society, Vol. 70, Issue. 03, p. 397.


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  • Bulletin of the Australian Mathematical Society, Volume 68, Issue 3
  • December 2003, pp. 449-459

On properties of semipreinvex functions

  • X. M. Yang (a1), X. Q. Yang and K. L. Teo (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700037850
  • Published online: 17 April 2009
Abstract

In this paper, we first discuss some basic properties of semipreinvex functions. We then show that the ratio of semipreinvex functions is semipreinvex, which extends earlier results by Khan and Hanson [6] and Craven and Mond [3]. Finally, saddle point optimality criteria are developed for a multiobjective fractional programming problem under semipreinvexity conditions.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]C.R. Bector , S. Chandra and M.K. Bector , ‘Generalized fractional programming duality: a parametric approach’, J. Optim. Theory Appl. 60 (1989), 243260.

[3]B.D. Craven and B. Mond , ‘Fractional programming with invexity’, in Progress in optimization, Appl. Optim. 30 (Kluwer Acad. Publ., Dordrecht, 1999), pp. 7989.

[4]M.A. Hanson , ‘On sufficiency of the Kuhn-Tucker conditions’, J. Math. Anal. Appl. 80 (1981), 544550.

[5]A.M. Geoffrion , ‘Proper efficiency and the theory of vector maximization’, J. Math. Anal. Appl. 22 (1968), 618630.

[6]Z.A. Kahn and M.A. Hanson , ‘On ratio invexity in mathematical programming’, J. Math. Anal. Appl. 205 (1997), 330336.

[8]M.A. Noor , ‘Nonconvex function and variational inequalities’, J. Optim. Theory Appl. 87 (1995), 615630.

[10]T. Weir and B. Mond , ‘Pre-invex functions in multiple objective optimization’, J. Math. Anal. Appl. 136 (1988), 2938.

[11]X.Q. Yang and G.Y. Chen , ‘A class of nonconvex functions and pre-variational inequalities’, J. Math. Anal. Appl. 169 (1992), 359373.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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