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Mathematical programming problems with quasi-convex objective functions

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Abstract

This paper generalizes results obtained by Arrow and Enthoven in [1] for functions of ClassC 2 on the non-negative orthant.

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References

  1. K.J. Arrow and A.C. Enthoven, “Quasi-concave programming,”Econometrica 29 (1961) 799–800.

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  2. R.W. Cottle and J.A. Ferland, “Matrix-theoretic criteria for the quasi-convexity and pseudoconvexity of quadratic functions,” Technical Report No. 70-6, Operations Research House, Stanford University, April 1970;Linear Algebra and Its Applications, to appear.

  3. R.W. Cottle and J.A. Ferland, “On pseudo-convex functions of nonnegative variables,”Mathematical Programming 1 (1971) 95–101.

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  4. H.W. Kuhn and A.W. Tucker, “Nonlinear programming,” in:Proceedings of the second Berkeley Symposium on mathematical statistics and probability, Ed. J. Neyman (University of California Press, Berkeley, California, 1951) pp. 481–493.

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Authors and Affiliations

  1. Université de Montreal, Montreal, Canada

    Jacques A. Ferland

Authors
  1. Jacques A. Ferland
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Additional information

This research was supported by Hydro—Quebec; University of Montreal; Office of Naval Research, Contract N-0014-67-A0112-001; National Science Foundation, Grant GP 25738.

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Ferland, J.A. Mathematical programming problems with quasi-convex objective functions. Mathematical Programming 3, 296–301 (1972). https://doi.org/10.1007/BF01585002

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  • DOI: https://doi.org/10.1007/BF01585002

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