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.
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.
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Dedicated to Professor R. Albrecht on the occasion of his 60th birthday
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Burmeister, W., Heß, W. & Schmidt, J.W. Convex spline interpolants with minimal curvature. Computing 35, 219–229 (1985). https://doi.org/10.1007/BF02260507
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DOI: https://doi.org/10.1007/BF02260507