Geodesic
Least Deviation Decomposition with Respect to a Pair of Convex Sets
Journal of convex analysis, Tome 6 (1999) no. 1, pp. 115-14

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

Let K1 and K2 be two nonempty closed convex sets in some normed space (H,' . '). This paper is concerned with the question of finding a "good" decomposition, with respect to K1 and K2, of a given element of the Minkowski sum K1+K2. We introduce and discuss the concept of least deviation decomposition. This concept is an extension of the Moreau orthogonal decomposition with respect to a pair of mutually polar cones. Techniques of convex analysis are applied to obtain some sensitivity and duality results related to the decomposition problem.
Classification : 41A65, 52A41
Mots-clés : Least deviation decomposition, convex analysis, Moreau orthogonal decomposition 
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     author = {D. T. Luc and J. E. Martinez-Legaz and A. Seeger},
     title = {Least {Deviation} {Decomposition} with {Respect} to a {Pair} of {Convex} {Sets}},
     journal = {Journal of convex analysis},
     pages = {115--14},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {1999},
     url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a7/}
}
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D. T. Luc; J. E. Martinez-Legaz; A. Seeger. Least Deviation Decomposition with Respect to a Pair of Convex Sets. Journal of convex analysis, Tome 6 (1999) no. 1, pp. 115-14. http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a7/