Geodesic
On the Fermat--Lagrange principle for mixed smooth convex extremal problems
Sbornik. Mathematics, Tome 192 (2001) no. 5, pp. 641-649

Voir la notice de l'article provenant de la source Math-Net.Ru

A simple geometric condition that can be attached to an extremal problem of a fairly general form included in a family of problems is indicated. This is used to demonstrate that the task of formulating a uniform condition for smooth convex problems can be satisfactorily accomplished. On the other hand, the necessity of this new condition of optimality is proved under certain technical assumptions. 
@article{SM_2001_192_5_a0,
     author = {J. Brinkhuis},
     title = {On the {Fermat--Lagrange} principle for mixed smooth convex extremal problems},
     journal = {Sbornik. Mathematics},
     pages = {641--649},
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     volume = {192},
     number = {5},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_5_a0/}
}
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J. Brinkhuis. On the Fermat--Lagrange principle for mixed smooth convex extremal problems. Sbornik. Mathematics, Tome 192 (2001) no. 5, pp. 641-649. http://geodesic.mathdoc.fr/item/SM_2001_192_5_a0/