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Set-valued mappings and enlargements of monotone operators / by Regina S. Burachik; Alfredo N. Iusem

By: Contributor(s): Resource type: Ressourcentyp: BuchBookPublisher number: 11930433Language: English Series: Springer optimization and its applications ; 8Publisher: New York ; NY : Springer, 2008Description: XVI, 293 S. : graph. DarstISBN:
  • 9780387697550
  • 0387697551
Other title:
  • set valued
Subject(s): Additional physical formats: 9780387697574 | Online-Ausg. u.d.T.: Set-Valued Mappings and Enlargements of Monotone Operators. Boston, MA : Springer Science+Business Media, LLC, 2008. Online-Ressource (XIV, 294 p, digital)DDC classification:
  • 515.724 22
  • 510
  • 510
MSC: MSC: *49-02 | 47H04 | 47H05 | 49J52 | 47-02RVK: RVK: SK 620LOC classification:
  • QA329.8
Contents:
Action note:
  • 3
Summary: Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, with the development of nonsmooth optimization, effective algorithms have been developed to solve these kinds of problems, such as nonsmooth variational inequalities. Several of these methods, such as bundle methods for variational problems, are fully developed and analyzed in this book. The first chapters provide a self-contained review of the basic notions and fundamental results in set-valued analysis, including set convergence and continuity of set-valued mappings together with many important results in infinite-dimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an in-depth introduction to monotone operators is developed, emphasizing results related to maximality of subdifferentials and of sums of monotone operators. Building on this foundational material, the second part of the monograph contains new results (all of them established during the last decade) on the concept of enlargements of monotone operators, with applications to variational inequalities, bundle-type methods, augmented Lagrangian methods, and proximal point algorithmsPPN: PPN: 1604723653
Holdings
Item type Home library Shelving location Call number Status Date due Barcode
Freihandbestand ausleihbar Fachbibliothek Mathematik Bibliothek / frei aufgestellt Untern.-forsch. / Bur Checked out 16.07.2025 36342156090
Total holds: 0

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