# 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 for
*n*-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, Proper
*D*-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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© Akadémiai Kiadó 1994