Additively decomposed quasiconvex functions

  title={Additively decomposed quasiconvex functions},
  author={G. Debreu and T. Koopmans},
  journal={Mathematical Programming},
  • 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
    97 Citations

    Figures and Topics from this paper

    Explore Further: Topics Discussed in This Paper

    On the existence of convex decompositions of partially separable functions
    • 30
    Is every radiant function the sum of quasiconvex functions?
    • A. Zaffaroni
    • Computer Science, Mathematics
    • Math. Methods Oper. Res.
    • 2004
    • 20
    • PDF
    Additively decomposed quasiconvex functions
    • 33
    • Highly Influenced
    On jet-convex functions and their tensor products
    • 4
    Generalized monotonicity of a separable product of operators: The multivalued case
    • 13
    • Highly Influenced
    Maximality and first-order criteria of r-monotone operators


    r-convex functions
    • M. Avriel
    • Mathematics, Computer Science
    • Math. Program.
    • 1972
    • 104
    A Review of Quasi-Convex Functions
    • 128
    Conjugacy in quasiconvex analysis
    • 20
    Pareto Optimality in Non-Convex Economies
    • 178
    Theory of Microeconomics
    • 73
    Cost and production functions
    • 1,712