Additively decomposed quasiconvex functions

@article{Debreu1982AdditivelyDQ,
  title={Additively decomposed quasiconvex functions},
  author={G. Debreu and T. Koopmans},
  journal={Mathematical Programming},
  year={1982},
  volume={24},
  pages={1-38}
}
  • G. Debreu, T. Koopmans
  • Published 1982
  • Mathematics, Computer Science
  • Mathematical Programming
  • Letf be a real-valued function defined on the product ofm finite-dimensional open convex setsX1, ⋯,Xm.Assume thatf is quasiconvex and is the sum of nonconstant functionsf1, ⋯,fm defined on the respective factor sets. Then everyfi is continuous; with at most one exception every functionfi is convex; if the exception arises, all the other functions have a strict convexity property and the nonconvex function has several of the differentiability properties of a convex function.We define the… CONTINUE READING
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