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  • 65H10  (2)
  • 65K05  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Unconstrained duals to partially separable constrained programs (1992)
    Springer
    Mathematical programming 56 (1992), S. 337-341 
    Details
    ISSN: 1436-4646
    Keywords: 90C25 ; 65K05 ; Lagrange dualization ; existence theorems ; numerical aspects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this note partially separable convex programs are dualized in such a way that, under certain assumptions, unconstrained concave duals arise. A return formula is given by which the solution of the primal is directly computed if a solution of the dual is known. Further, the solvability of both the primal and the dual is shown to depend essentially on the behaviour of the lower dimensional programs for determining the Fenchel conjugates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580906
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Convex spline interpolants with minimal curvature (1985)
    Springer
    Computing 35 (1985), S. 219-229 
    Details
    ISSN: 1436-5057
    Keywords: 65K05 ; 65D07 ; 90C20 ; 41A15 ; Existence conditions ; quadratic programming ; dual optimization problem ; tridiagonal Hessian ; Newton's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Problem, konvexe Interpolationssplines mit minimaler mittlerer Krümmung zu ermitteln, führt auf eine speziell strukturierte quadratische Optimierungsaufgabe. In der vorliegenden Note wird eine zugehörige duale Aufgabe aufgestellt, die ohne Nebenbedingungen auskommt, deren Zielfunktion stückweise quadratisch ist und die daher eine effektive numerische Behandlung erlaubt.
    Notes: Abstract The problem of finding convex spline interpolants with minimal mean curvature leads to a quadratic optimization problem of special structure. In the present note a corresponding dual problem without constraints is derived. Its objective function is piecewise quadratic and therefore admits an effective numerical treatment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02260507
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences III (1983)
    Springer
    Computing 30 (1983), S. 157-169 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 15A48 ; Iterative parallel processes ; best individualR-orders ; ordered positive decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für konvergente Folgen {x n,1 },...,{x n,s }, welche über ein System (2) von Ungleichungen miteinander verkoppelt sind, werden die besten individuellenR-Ordnungen τ1,...,τ s bestimmt. Dazu wird gezeigt, daß diese gleich den Spektralradien von bestimmten Matrizen sind, welche aus Exponenten in (2) gebildet werden.
    Notes: Abstract For convergent sequences {x n,1 },...{x n,s } coupled by a system (2) of inequalities the optimal individualR-orders τ1,...,τ s are determined as the spectral radii of certain matrices composed of exponents appearing in (2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02280786
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Determination of the cone radius for positive concave operators (1984)
    Springer
    Computing 33 (1984), S. 37-49 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 90C30 ; 15A48 ; Iterative processes ; bestR-orders ; cone radius of concave operators ; spectral radii ; partial ordering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Berechnung der bestenR-Ordnung von Folgen aus iterativen Näherungsverfahren führt auf die Ermittlung des hier eingeführten Kegelradius bestimmter konkaver Operatoren. Das Hauptergebnis der Arbeit ist die Darstellung des Kegelradius als Infimum der Spektralradien aller den konkaven Operator majorisierenden linearen Operatoren. Diese Charakterisierung ist von numerischem Intersse.
    Notes: Abstract The computation of bestR-orders of sequences produced by iterative methods leads to the determination of the cone radius of certain concave operators. The main result of the paper is the representation of the cone radius as the infimum of spectral radii of all linear operators majorizing the concave operator. This characterization is of numerical interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243074
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    Paper (German National Licenses)
    Fulltext
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