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  • Electronic Resource  (2)
  • 1
    Electronic Resource
    Electronic Resource
    A Geometric Approach to Global Optimization (1999)
    Springer
    Journal of global optimization 15 (1999), S. 109-126 
    Details
    ISSN: 1573-2916
    Keywords: Reverse convex constraints ; Geometric approach ; Discretization ; Piecewise linear programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider the problem of optimizing a piecewise-linear objective function over a non-convex domain. In particular we do not allow the solution to lie in the interior of a prespecified region R. We discuss the geometrical properties of this problems and present algorithms based on combinatorial arguments. In addition we show how we can construct quite complicated shaped sets R while maintaining the combinatorial properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008367608172
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    HYPERPLANE TRANSVERSALS OF HOMOTHETICAL, CENTRALLY SYMMETRIC POLYTOPES (2000)
    Springer
    Periodica mathematica Hungarica 39 (2000), S. 73-81 
    Details
    ISSN: 1588-2829
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P ⊂ R n be a centrally symmetric, convex n-polytope with 2r vertices, n ≥ 2. Let P be a family of m ≥ n + 1 homothetical copies of P. Based on an algorithmical approach to center hyperplanes of finite point sets in Minkowski spaces with polyhedral norms, we show that a hyperplane transversal of all members of P (if it exists) can be found in O(rm) time when the dimension n is fixed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004886722459
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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