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  • 1
    Electronic Resource
    Electronic Resource
    Superlinear primal-dual affine scaling algorithms for LCP (1995)
    Springer
    Mathematical programming 69 (1995), S. 311-333 
    Details
    ISSN: 1436-4646
    Keywords: Interior-point methods ; Primal-dual affine scaling ; Linear programming ; Linear complementarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe an interior-point algorithm for monotone linear complementarity problems in which primal-dual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Q-order up to (but not including) two. The technique is shown to be consistent with a potential-reduction algorithm, yielding the first potential-reduction algorithm that is both globally and superlinearly convergent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585562
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A simplified global convergence proof of the affine scaling algorithm (1993)
    Springer
    Annals of operations research 46-47 (1993), S. 443-482 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper presents a simplified and self-contained global convergence proof for the affine scaling algorithm applied to degenerate linear programming problems. Convergence of the sequence of dual estimates to the center of the optimal dual face is also proven. In addition, we give a sharp rate of convergence result for the sequence of objective function values. All these results are proved with respect to the long step version of the affine scaling algorithm in which we move a fraction λ, where λ ∈ (0,2/3), of the step to the boundary of the feasible region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023109
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    Paper (German National Licenses)
    Fulltext
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