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On feasible sets defined through Chebyshev approximation

Author

Listed:
  • Francisco Guerra
  • Miguel Jiménez

Abstract

LetZ be a compact set of the real space ℜ with at leastn + 2 points;f,h1,h2:Z → ℜ continuous functions,h1,h2 strictly positive andP(x,z),x≔(x 0 ,...,x n ) τ ε ℜ n+1 ,z ε ℜ, a polynomial of degree at mostn. Consider a feasible setM ≔ {x ε ℜ n+1 ∣∀z εZ, −h 2 (z) ≤P(x, z)−f(z)≤h 1 (z)}. Here it is proved the null vector 0 of ℜ n+1 belongs to the compact convex hull of the gradients ± (1,z,...,z n ), wherez εZ are the index points in which the constraint functions are active for a givenx* ε M, if and only ifM is a singleton. Copyright Physica-Verlag 1998

Suggested Citation

  • Francisco Guerra & Miguel Jiménez, 1998. "On feasible sets defined through Chebyshev approximation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(2), pages 255-264, June.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:2:p:255-264
    DOI: 10.1007/BF01194400
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    Cited by:

    1. Goberna, M. A. & Lopez, M. A., 2002. "Linear semi-infinite programming theory: An updated survey," European Journal of Operational Research, Elsevier, vol. 143(2), pages 390-405, December.

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