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  • 90C25  (2)
  • 65 D 07  (1)
  • 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
    Constrained smoothing of histograms by quadratic splines (1992)
    Springer
    Computing 48 (1992), S. 97-107 
    Details
    ISSN: 1436-5057
    Keywords: 65D10 ; 41A15 ; 90C25 ; FunctionalsK 2 andK ∞, constraints like convexity or monotonicity ; linear programs ; partially separable programs and dualization ; Fenchel conjugates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zum Glätten von Histogrammen unter Nebendedingungen wie Konvexität oder Monotonie werden die ZielfunktionaleK 2 undK ∞ vorgeschlagen, welche dem bekannten Schoenberg-Funktional von der Datenglättung nachgebildet sind. Bei Verwendung von quadratischen Splines erhält man strukturierte, endlichdimensionale Optimierungsaufgaben. Auftretende partiell separable, konvexe Aufgaben können durch Dualisierung einer effektiven numerischen Behandlung zugeführt werden.
    Notes: Abstract For smoothing histograms under constraints like convexity or monotonicity, in this paper the functionalsK 2 andK ∞ are proposed which can be considered as extensions of the Schoenberg functional known from data smoothing. When using quadratic splines we are led to structured finite dimensional programming problems. Occuring partially separable convex programs can be solved effectively via dualization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241708
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Positive, monotone, andS-convexC 1-interpolation on rectangular grids (1992)
    Springer
    Computing 48 (1992), S. 363-371 
    Details
    ISSN: 1436-5057
    Keywords: 65 D 07 ; 41 A 15 ; 41 A 63 ; Shape preservingC 1-interpolation ; special rational biquadratic splines ; construction by a search procedure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit befaßt sich mit formerhaltenderC 1-Interpolation von Daten auf Rechteckgittern. Bei Verwendung von speziellen rational-biquadratischen Splines werden Bedingungen hergeleitet, welche hinreichend für die Positität, Monotonie undS-Konvexität sind und welche sich darüber hinaus erfüllen lassen, sofern die Rationalitätsparameter hinreichend groß sind.
    Notes: Abstract This paper is concerned with shape preservingC 1-interpolation of data sets given on rectangular grids. Using special rational biquadratic splines, criteria are derived which are sufficient for the positivity, monotonicity, andS-convexity and which, in addition, are satisfied for sufficiently large rationality parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238643
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    Paper (German National Licenses)
    Fulltext
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