Generalized characterization of the convex envelope of a function
RAIRO - Operations Research - Recherche Opérationnelle, Volume 36 (2002) no. 1, pp. 95-100.

We investigate the minima of functionals of the form

[a,b] g(u ˙(s))ds
where g is strictly convex. The admissible functions u:[a,b] are not necessarily convex and satisfy uf 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.

DOI: 10.1051/ro:2002007
Keywords: convex envelope, optimization, strict convexity, cost function
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     author = {Kadhi, Fethi},
     title = {Generalized characterization of the convex envelope of a function},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {95--100},
     publisher = {EDP-Sciences},
     volume = {36},
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     doi = {10.1051/ro:2002007},
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Kadhi, Fethi. Generalized characterization of the convex envelope of a function. RAIRO - Operations Research - Recherche Opérationnelle, Volume 36 (2002) no. 1, pp. 95-100. doi : 10.1051/ro:2002007. http://archive.numdam.org/articles/10.1051/ro:2002007/

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