Geodesic
Proximal Points are on the Fast Track
Journal of convex analysis, Tome 9 (2002) no. 2, pp. 563-579 Cet article a éte moissonné depuis la source Heldermann Verlag

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For a convex function, we consider a space decomposition that allows us to identify a subspace on which a Lagrangian related to the function appears to be smooth. We study a particular trajectory, that we call a fast track, on which a certain second-order expansion of the function can be obtained. We show how to obtain such fast tracks for a general class of convex functions having primal-dual gradient structure. Finally, we show that for a point near a minimizer its corresponding proximal point is on the fast track.
Classification : 49K35, 49M27, 65K10, 90C25
Mots-clés : Convex minimization, proximal points, second-order derivatives, VU-decomposition 
@article{JCA_2002_9_2_JCA_2002_9_2_a14,
     author = {R. Mifflin and C. Sagastiz\'abal},
     title = {Proximal {Points} are on the {Fast} {Track}},
     journal = {Journal of convex analysis},
     pages = {563--579},
     year = {2002},
     volume = {9},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a14/}
}
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R. Mifflin; C. Sagastizábal. Proximal Points are on the Fast Track. Journal of convex analysis, Tome 9 (2002) no. 2, pp. 563-579. http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a14/