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  • 1
    Electronic Resource
    Electronic Resource
    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
    Keywords: Potential function ; multiplicative penalty function ; convexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580721
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A linear-time algorithm for linearL 1 approximation of points (1989)
    Springer
    Algorithmica 4 (1989), S. 77-96 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Modified pruning technique ; LinearL 1 approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we present a linear-time algorithm for approximating a set ofn points by a linear function, or a line, that minimizes theL 1 norm. The algorithmic complexity of this problem appears not to have been investigated, although anO(n 3) naive algorithm can be easily obtained based on some simple characteristics of an optimumL 1 solution. Our linear-time algorithm is optimal within a constant factor and enables us to use linearL 1 approximation of many points in practice. The complexity ofL 1 linear approximation of a piecewise linear function is also touched upon.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01553880
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    Paper (German National Licenses)
    Fulltext
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