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Generalized Characterizationof the Convex Envelope of a Function

Published online by Cambridge University Press:  15 July 2002

Fethi Kadhi
Fethi Kadhi*
Affiliation:
Preparatory Institute of Engineering Studies, P.O. Box 805, 3018 Sfax, Tunisia.
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Abstract

We investigate the minima of functionals of the form $$\int_{[a,b]}g(\dot u(s)){\rm d}s$$ where g is strictly convex. The admissible functions $u:[a,b]\longrightarrow\mathbb{R}$ are not necessarily convex and satisfy $u\leq f$ on [a,b], u(a)=f(a), u(b)=f(b), f is a fixed function on [a,b].We show that the minimum is attained by $\bar f$ , the convex envelope of f.

Keywords

Convex envelopeoptimizationstrict convexitycost function.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 1 , January 2002 , pp. 95 - 100
Copyright
© EDP Sciences, 2002

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References

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