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  • 1
    Electronic Resource
    Electronic Resource
    Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems (1986)
    Springer
    Mathematical programming 35 (1986), S. 173-192 
    Details
    ISSN: 1436-4646
    Keywords: Computational complexity ; average running time ; simplex algorithm ; linear programming ; linear complementarity problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a particular pivoting algorithm, which we call the lexicographic Lemke algorithm, takes an expected number of steps that is bounded by a quadratic inn, when applied to a random linear complementarity problem of dimensionn. We present two probabilistic models, both requiring some nondegeneracy and sign-invariance properties. The second distribution is concerned with linear complementarity problems that arise from linear programming. In this case we give bounds that are quadratic in the smaller of the two dimensions of the linear programming problem, and independent of the larger. Similar results have been obtained by Adler and Megiddo.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580646
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  • 2
    Electronic Resource
    Electronic Resource
    An O(n 3 L) adaptive path following algorithm for a linear complementarity problem (1991)
    Springer
    Mathematical programming 52 (1991), S. 587-595 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; linear complementarity problem ; interior point algorithms ; path following algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we propose an O(n 3 L) algorithm which is a modification of the path following algorithm [8] for a linear complementarity problem. The path following algorithm has to take a short step size in each iteration in order to bound the number of overall arithmetic operations by O(n 3 L). In practical computation, we can determine the step size adaptively. Mizuno, Yoshise, and Kikuchi [11] reported that such an adaptive algorithm required about O(L) iterations for some test problems. Here we show that we can use a rank one update technique in the adaptive algorithm so that the number of overall arithmetic operations is theoretically bounded by O(n 3 L).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582906
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