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  • Chebyshev approximation  (1)
  • nonlinear optimization  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On feasible sets defined through Chebyshev approximation (1998)
    Springer
    Mathematical methods of operations research 47 (1998), S. 255-264 
    Details
    ISSN: 1432-5217
    Keywords: Chebyshev approximation ; semi-infinite programming ; constraint qualification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194400
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A parametric embedding for the finite minimax problem (1999)
    Springer
    Mathematical methods of operations research 49 (1999), S. 359-371 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Minimax problems ; nonlinear optimization ; parametric optimization ; parametric embedding ; pathfollowing methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We consider unconstrained finite minimax problems where the objective function is described as a maximum of functions f k∈C 3(ℜn,ℜ). We propose a parametric embedding for the minimax problem and, assuming that the corresponding parametric optimization problem belongs to the generic class of Jongen, Jonker and Twilt, we show that if one applies pathfollowing methods (with jumps) to the embedding in the convex case (in the nonconvex case) one obtains globally convergent algorithms. Furthermore, we prove under usual assumptions on the minimax problem that pathfollowing methods applied to a perturbed parametric embedding of the original minimax problem yield globally convergent algorithms for almost all perturbations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050054
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    Paper (German National Licenses)
    Fulltext
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