Geodesic
Relating U-Lagrangians to Second-Order Epi-Derivatives and Proximal Tracks
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 81-93

Voir la notice de l'article provenant de la source Heldermann Verlag

We make use of VU-space decomposition theory to connect three minimization-oriented objects. These objects are U-Lagrangians obtained from minimizing a function over V-space, proximal points depending on minimization over Rn = U + V, and epi-derivatives determined by lower limits associated with epigraphs. We relate second-order epi-derivatives of a function to the Hessian of its associated U -Lagrangian. We also show that the function's proximal points are on a trajectory determined by certain V-space minimizers.
Classification : 90C31, 49J52, 65K10, 49J53
Mots-clés : U-Lagrangian, proximal point, second-order epi-derivatives 
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     title = {Relating {\protect\emph{U}-Lagrangians} to {Second-Order} {Epi-Derivatives} and {Proximal} {Tracks}},
     journal = {Journal of convex analysis},
     pages = {81--93},
     publisher = {mathdoc},
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     number = {1},
     year = {2005},
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R. Mifflin; C. Sagastizabal. Relating U-Lagrangians to Second-Order Epi-Derivatives and Proximal Tracks. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 81-93. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a4/