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  • 1
    Electronic Resource
    Electronic Resource
    A Long-step barrier method for convex quadratic programming (1993)
    Springer
    Algorithmica 10 (1993), S. 365-382 
    Details
    ISSN: 1432-0541
    Keywords: Convex quadratic programming ; Interior-point method ; Logarithmic barrier function ; Polynomial algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we propose a long-step logarithmic barrier function method for convex quadratic programming with linear equality constraints. After a reduction of the barrier parameter, a series of long steps along projected Newton directions are taken until the iterate is in the vicinity of the center associated with the current value of the barrier parameter. We prove that the total number of iterations isO(√nL) orO(nL), depending on how the barrier parameter is updated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01769704
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Primal-dual target-following algorithms for linear programming (1996)
    Springer
    Annals of operations research 62 (1996), S. 197-231 
    Details
    ISSN: 1572-9338
    Keywords: Interior-point method ; primal-dual method ; target-following ; centering ; Dikin steps
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we propose a method for linear programming with the property that, starting from an initial non-central point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow paths that in the limit are tangential to the central path. Together with the convergence analysis, we provide a general framework which enables us to analyze various primal-dual algorithms in the literature in a short and uniform way.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02206817
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A polynomial method of approximate centers for linear programming (1992)
    Springer
    Mathematical programming 54 (1992), S. 295-305 
    Details
    ISSN: 1436-4646
    Keywords: Interior-point method ; linear programming ; Karmarkar's method ; polynomial-time algorithm ; logarithmic barrier function ; path-following method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a path-following algorithm for the linear programming problem with a surprisingly simple and elegant proof of its polynomial behaviour. This is done both for the problem in standard form and for its dual problem. We also discuss some implementation strategies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586056
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A sufficient condition for self-concordance, with application to some classes of structured convex programming problems (1995)
    Springer
    Mathematical programming 69 (1995), S. 75-88 
    Details
    ISSN: 1436-4646
    Keywords: Interior-point method ; Barrier function ; Dual geometric programming ; (Extended) entropy programming ; Primal and duall p -programming ; Relative Lipschitz condition ; Scaled Lipschitz condition ; Self-concordance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently a number of papers were written that present low-complexity interior-point methods for different classes of convex programs. The goal of this article is to show that the logarithmic barrier function associated with these programs is self-concordant. Hence the polynomial complexity results for these convex programs can be derived from the theory of Nesterov and Nemirovsky on self-concordant barrier functions. We also show that the approach can be applied to some other known classes of convex programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585553
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    Paper (German National Licenses)
    Fulltext
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