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  • 90C25  (2)
  • Existence conditions  (2)
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  • 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)
    Fulltext
  • 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
    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)
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  • 4
    Electronic Resource
    Electronic Resource
    Positive interpolation with rational quadratic splines (1987)
    Springer
    Computing 38 (1987), S. 261-267 
    Details
    ISSN: 1436-5057
    Keywords: 65D07 ; 41A15 ; Existence conditions ; construction os positive splines ; minimization of the curvature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Unter positiver Interpolation wird die Aufgabenstellung verstanden, zur einer nichtnegativen Datenmenge nichtnegative Interpolierende zu konstruieren. Im Fallen rational-quadratischer Splines wird eine notwendige und hinreichende Bedingung für die Durchführbarkeit positiver Interpolation hergeleitet, und es wird gezeigt, daß diese sich bei passender Wahl der vorkommenden Parameter stets erfüllen läßt.
    Notes: Abstract A necessary and sufficient criterion is presented under which the property of positivity carry over from the data set to rational quadratic spline interpolants. The criterion can always be satisfied if the occuring parameters are properly chosen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240100
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    Paper (German National Licenses)
    Fulltext
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