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Generalized characterization of the convex envelope of a function

Fethi Kadhi — 2002

RAIRO - Operations Research - Recherche Opérationnelle

We investigate the minima of functionals of the form [ a , b ] g ( u ˙ ( s ) ) d s where g is strictly convex. The admissible functions u : [ a , b ] are not necessarily convex and satisfy u 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 f ¯ , the convex envelope of f .

Generalized Characterization of the Convex Envelope of a Function

Fethi Kadhi — 2010

RAIRO - Operations Research

We investigate the minima of functionals of the form [ a , b ] g ( u ˙ ( s ) ) d s where is strictly convex. The admissible functions u : [ a , b ] are not necessarily convex and satisfy u f on , , , is a fixed function on . We show that the minimum is attained by f ¯ , the convex envelope of .

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