rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Set-Valued Mappings and Enlargements of Monotone Operators
  name:
    name part: Burachik, Regina S.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Iusem, Alfredo N.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 294 p. 15 illus. online resource.
  abstract: 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 algorithms. Audience This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as point-to-set operators, variational inequalities, general equilibrium theory, and nonsmooth optimization, among others. Containing extensive exercises and examples throughout the text, the first four chapters of the book can also be used for a one-quarter course in set-valued analysis and maximal monotone operators for graduate students…
  table of contents: Set Convergence and Point-to-Set Mappings -- Convex Analysis and Fixed Point Theorems -- Maximal Monotone Operators -- Enlargements of Monotone Operators -- Recent Topics in Proximal Theory.
  note: by Regina S. Burachik, Alfredo N. Iusem.
  subject:
    topic: Mathematics
  subject:
    topic: Operations research
  subject:
    topic: Decision making
  subject:
    topic: Functional analysis
  subject:
    topic: Operator theory
  subject:
    topic: Mathematical optimization
  subject:
    topic: Calculus of variations
  subject:
    topic: Management science
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Optimization
  subject:
    topic: Operator Theory
  subject:
    topic: Operations Research, Management Science
  subject:
    topic: Operation Research/Decision Theory
  subject:
    topic: Calculus of Variations and Optimal Control; Optimization
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Optimization and Its Applications, 8
  identifier: 9780387697574
  identifier: http://dx.doi.org/10.1007/978-0-387-69757-4
  record info:
    record creation date: 100301
    record change date: 20151204162257.0
    record identifier: 978-0-387-69757-4