Geodesic
Proper Approximate Solutions and ε-Subdifferentials in Vector Optimization: Moreau-Rockafellar Type Theorems
Journal of convex analysis, Tome 21 (2014) no. 3, pp. 857-886.

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

We provide Moreau-Rockafellar type theorems for a kind of proper ε-subdifferential of vector-valued mappings. For this aim, we introduce and study a new notion of approximate strong solution of a vector optimization problem, a new strong ε-subdifferential based on this type of approximate strong solutions, and a new regularity condition. Finally, as a consequence of the obtained exact sum rules, the gap between the strong and the proper ε-subdifferentials is provided.
Classification : 90C48, 90C25, 90C29, 49J52, 49K27
Mots-clés : Vector optimization, proper epsilon-efficiency, proper epsilon-subdifferential, nearly subconvexlikeness, strong epsilon-efficiency, strong epsilon-subdifferential, linear scalarization, epsilon-subdifferential 
@article{JCA_2014_21_3_JCA_2014_21_3_a15,
     author = {C. Guti\'errez and L. Huerga and B. Jim\'enez and V. Novo},
     title = {Proper {Approximate} {Solutions} and {\ensuremath{\varepsilon}-Subdifferentials} in {Vector} {Optimization:} {Moreau-Rockafellar} {Type} {Theorems}},
     journal = {Journal of convex analysis},
     pages = {857--886},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a15/}
}
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C. Gutiérrez; L. Huerga; B. Jiménez; V. Novo. Proper Approximate Solutions and ε-Subdifferentials in Vector Optimization: Moreau-Rockafellar Type Theorems. Journal of convex analysis, Tome 21 (2014) no. 3, pp. 857-886. http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a15/