On feasible sets defined through Chebyshev approximation

Francisco Guerra () and Miguel Jiménez ()

Mathematical Methods of Operations Research, 1998, vol. 47, issue 2, 255-264

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

Keywords: Chebyshev approximation; semi-infinite programming; constraint qualification (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/BF01194400

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