Geodesic
On the Cutting Plane Property and the Bregman Proximal Point Algorithm
Journal of convex analysis, Tome 18 (2011) no. 3, pp. 601-619
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The Bregman-function-based Proximal Point Algorithm (BPPA) for solving variational inequalities is considered. In this framework the customary assumption of the cutting plane property (CPP) of the related operator is investigated. Since this property cannot be expected in saddle-point-problems, it should be considered as rather restrictive. This paper contributes to the situation when the CPP fails to hold. For this situation, interior proximal(-like) methods have only been constructed for polyhedral sets up to now. 
@article{JCA_2011_18_3_JCA_2011_18_3_a0,
     author = {N. Langenberg},
     title = {On the {Cutting} {Plane} {Property} and the {Bregman} {Proximal} {Point} {Algorithm}},
     journal = {Journal of convex analysis},
     pages = {601--619},
     year = {2011},
     volume = {18},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a0/}
}
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N. Langenberg. On the Cutting Plane Property and the Bregman Proximal Point Algorithm. Journal of convex analysis, Tome 18 (2011) no. 3, pp. 601-619. http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a0/