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  • Interior method  (1)
  • Potential function  (1)
  • Power diagram  (1)
  • 1
    Digitale Medien
    Digitale Medien
    On the convexity of the multiplicative version of Karmarkar's potential function (1988)
    Springer
    Mathematical programming 40 (1988), S. 29-32 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Potential function ; multiplicative penalty function ; convexity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Karmarkar's potential function is quasi-convex, but not convex. This note investigates the multiplicative version of the potential function, and shows that it is not necessarily convex in general, but is strictly convex when the corresponding feasible region is bounded. This implies that the multiplicative version of the potential function in Karmarkar's algorithm is convex, since it works on a simplex.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580721
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  • 2
    Digitale Medien
    Digitale Medien
    A multiplicative barrier function method for linear programming (1986)
    Springer
    Algorithmica 1 (1986), S. 455-482 
    Details
    ISSN: 1432-0541
    Schlagwort(e): Linear programming ; Interior method ; Barrier function ; Newton method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A simple Newton-like descent algorithm for linear programming is proposed together with results of preliminary computational experiments on small- and medium-size problems. The proposed algorithm gives local superlinear convergence to the optimum and, experimentally, shows global linear convergence. It is similar to Karmarkar's algorithm in that it is an interior feasible direction method and self-correcting, while it is quite different from Karmarkar's in that it gives superlinear convergence and that no artificial extra constraint is introduced nor is protective geometry needed, but only affine geometry suffices.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01840457
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  • 3
    Digitale Medien
    Digitale Medien
    Computing the volume of the union of spheres (1988)
    Springer
    The visual computer 3 (1988), S. 323-328 
    Details
    ISSN: 1432-2315
    Schlagwort(e): Union of Spheres ; Volumes ; Laguerre Voronoid diagram ; Power diagram
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Abstract OnO(n 2) exact algorithm is given for computing the volume of a set ofn spheres in space. The algorithm employs the Laguerre Voronoi (power) diagram and a method for computing the volume of the intersection of a simplex and a sphere exactly. We give a new proof of a special case of a conjecture, popularized by Klee, concerning the change in volume as the centres of the spheres become further apart.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01901190
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