An Additive Subfamily of Enlargements of a Maximally Monotone Operator

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• 作者：Regina S. Burachik ; Juan Enrique Martínez-Legaz…
• 关键词：Maximally monotone operator ; ε ; subdifferential mapping ; Subdifferential operator ; Convex lower semicontinuous function ; Fitzpatrick function ; Enlargement of an operator ; Brndsted ; Rockafellar enlargements ; Additive enlargements ; Brndsted ; Rockafellar property ; Fenchel ; Young function ; 49J52 ; 48N15 ; 90C25 ; 90C30 ; 90C46
• 刊名：Set-Valued and Variational Analysis
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：23
• 期：4
• 页码：643-665
• 全文大小：374 KB
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  30.Rockafellar, R.T.: C
• 作者单位：Regina S. Burachik (1)
  Juan Enrique Martínez-Legaz (2)
  Mahboubeh Rezaie (3)
  Michel Théra (4) (5)
  
  1. School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes, SA, 5095, Australia
  2. Departament d’Economia i d’Historia Economica, Universitat Autonoma de Barcelona, Barcelona, Spain
  3. University of Isfahan, Isfahan, Iran
  4. Laboratoire XLIM, Université de Limoges, 123, Avenue Albert Thomas, 87060, Limoges Cedex, France
  5. Centre for Informatics and Applied Optimisation, Federation University, Mount Helen Campus, PO Box 663, Ballarat, VIC, 3353, Australia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1877-0541

文摘

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical ε-subdifferential enlargement widely used in convex analysis. We also recover the ε-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the ε-subdifferential enlargement. Keywords Maximally monotone operator ε-subdifferential mapping Subdifferential operator Convex lower semicontinuous function Fitzpatrick function Enlargement of an operator Brndsted- Rockafellar enlargements Additive enlargements Brndsted- Rockafellar property Fenchel-Young function