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  • Linear programming  (1)
  • Quadratic programming  (1)
  • linear constraints  (1)
  • 1
    Digitale Medien
    Digitale Medien
    A parameterized hessian quadratic programming problem (1986)
    Springer
    Annals of operations research 5 (1986), S. 371-394 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Quadratic programming ; active set algorithms ; parametric Hessian matrix
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract We present a general active set algorithm for the solution of a convex quadratic programming problem having a parametrized Hessian matrix. The parametric Hessian matrix is a positive semidefinite Hessian matrix plus a real parameter multiplying a symmetric matrix of rank one or two. The algorithm solves the problem for all parameter values in the open interval upon which the parametric Hessian is positive semidefinite. The algorithm is general in that any of several existing quadratic programming algorithms can be extended in a straightforward manner for the solution of the parametric Hessian problem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02022081
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  • 2
    Digitale Medien
    Digitale Medien
    The simplex method and unrestricted variables (1985)
    Springer
    Journal of optimization theory and applications 45 (1985), S. 33-39 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Linear programming ; simplex method ; unrestricted variables ; simplex multipliers ; LU-factorization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Suppose that the simplex method is applied to a linear programming problem havingm equality constraints andr unrestricted variables. We give a method of performing the steps of the simplex method which reduces the arithmetic operation count byrm at each iteration. This savings in operations is achieved, since the method does not update the rows of the basis inverse associated with the unrestricted variables. Similar computational savings are achieved when the method is applied to the updating of anLU-factorization of the basis matrix.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940811
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  • 3
    Digitale Medien
    Digitale Medien
    A degenerate extreme point strategy for the classification of linear constraints as redundant or necessary (1989)
    Springer
    Journal of optimization theory and applications 62 (1989), S. 225-237 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Redundancy ; degeneracy ; linear constraints ; linear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This paper presents a degenerate extreme point strategy for active set algorithms which classify linear constraints as either redundant or necessary. The strategy makes use of an efficient method for classifying constraints active at degenerate extreme points. Numerical results indicate that significant savings in the computational effort required to classify the constraints can be achieved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00941055
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