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Alternative theorems and saddlepoint results for convex programming problems of set functions with values in ordered vector spaces

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References

  1. C. Berge and A. Ghouila-Houri,Programming, Games and Transportation Networks, Wiley and Sons (N. Y., 1965).

    Google Scholar 

  2. J. H. Chou, W. S. Hsia and T. Y. Lee, On multiple objective programming problems with set functions,J. Math. Anal. Appl.,105 (1985), 383–394.

    Google Scholar 

  3. J. H. Chou, W. S. Hsia and T. Y. Lee, Second order optimality conditions for mathematical programming with set functions,J. Austral. Math. Soc. (Ser. B),26 (1985), 284–292.

    Google Scholar 

  4. J. H. Chou, W. S. Hsia and T. Y. Lee, Epigraphs of convex set functions,J. Math. Anal. Appl.,118 (1986), 247–254.

    Google Scholar 

  5. J. H. Chou, W. S. Hsia and T. Y. Lee, Convex programming with set functions,Rocky Mountain J. Math.,17 (1987), 535–543.

    Google Scholar 

  6. H. W. Corley, Optimization theory forn-set functions,J. Math. Anal. Appl.,127 (1987), 193–205.

    Google Scholar 

  7. B. D. Craven and J. J. Koliha, Generalizations of Farkas' theorems,SIAM J. Math. Anal.,8 (1977), 983–997.

    Google Scholar 

  8. Ky Fan, On systems of linear inequalities,Linear Inequalities and Related System (Ann. of Math. Studies 38), Edited by H. W. Kuhn and A. W. Tucker, Princeton Univ. Press (Princeton, N. J., 1956), pp. 99–156.

    Google Scholar 

  9. W. S. Hsia and T. Y. Lee, ProperD-solutions of multiobjective programming problems with set functions,J. Optim. Theory Appl.,53 (1987), 247–258.

    Google Scholar 

  10. H. C. Lai and S. S. Yang, Saddle point and duality in the optimization theory of convex functions,J. Austral. Math. Soc. (Ser. B),24 (1982), 130–137.

    Google Scholar 

  11. H. C. Lai, S. S. Yang and Goerge R. Hwang, Duality in mathematical programming of set functions — On Fenchel duality theorem,J. Math. Anal. Appl.,95 (1983), 223–234.

    Google Scholar 

  12. H. C. Lai and C. P. Ho, Duality theorem of nondifferentiable convex multiobjective programming,J. Optim. Theory Appl.,50 (1986), 407–420.

    Google Scholar 

  13. H. C. Lai and L. J. Lin, Moreau-Rockafellar type theorem for convex set functions,J. Math. Anal. Appl.,132 (1988); 558–571.

    Google Scholar 

  14. H. C. Lai and L. J. Lin, The Fenchel-Moreau theorem for set functions,Proc. Amer. Math. Soc.,103 (1988), 85–90.

    Google Scholar 

  15. H. C. Lai and L. J. Lin, Optimality for set functions with values in ordered vector spaces,J. Optim. Theory Appl.,63 (1989), 371–389.

    Google Scholar 

  16. H. C. Lai and L. S. Yang, Strong duality for infinite-dimensional vector-valued programming problems,J. Optim. Theory Appl.,62 (1989), 449–466.

    Google Scholar 

  17. O. L. Mangasarian,Nonlinear Programming, McGraw-Hill Co. (N. Y., 1969).

    Google Scholar 

  18. R. J. T. Morris, Optimal constrained selection of a measurable subset,J. Math. Anal. Appl.,70 (1979), 546–562.

    Google Scholar 

  19. J. Zowe, A duality theorem for a convex programming problem in order complete vector lattices,J. Math. Anal. Appl.,50 (1975), 273–287.

    Google Scholar 

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This research was partially supported by NSC Taiwan. This paper was partly written when the first author was a professor in the University of Cape Town.

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Lai, H.C., Szilágyi, P. Alternative theorems and saddlepoint results for convex programming problems of set functions with values in ordered vector spaces. Acta Math Hung 63, 231–241 (1994). https://doi.org/10.1007/BF01874130

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  • DOI: https://doi.org/10.1007/BF01874130

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