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  • 1
    Digitale Medien
    Digitale Medien
    Modifications and implementation of the ellipsoid algorithm for linear programming (1982)
    Springer
    Mathematical programming 23 (1982), S. 1-19 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Ellipsoid Algorithm ; Linear Programming ; Polynomial Boundedness ; Khachian's Method ; Linear Inequalities
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We give some modifications of the ellipsoid algorithm for linear programming and describe a numerically stable implementation. We are concerned with practical problems where user-supplied bounds can usually be provided. Our implementation allows constraint dropping and updates bounds on the optimal value, and should be able to terminate with an indication of infeasibility or with a provably good feasible solution in a moderate number of iterations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01583776
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Curvilinear path steplength algorithms for minimization which use directions of negative curvature (1980)
    Springer
    Mathematical programming 18 (1980), S. 31-40 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Step-size Procedures ; Line Search ; Gradient Methods ; Unconstrained Minimization ; Negative Curvature
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The Armijo and Goldstein step-size rules are modified to allow steps along a curvilinear path of the formx(α) + x + αs + α2 d, wherex is the current estimate of the minimum,s is a descent direction andd is a nonascent direction of negative curvature. By using directions of negative curvature when they exist, we are able to prove, under fairly mild assumptions, that the sequences of iterates produced by these algorithms converge to stationary points at which the Hessian matrix of the objective function is positive semidefinite.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588294
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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    Artikel (Nationallizenzen)
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