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: Variational Analysis and Generalized Differentiation I
    sub title: Basic Theory
  name:
    name part: Mordukhovich, Boris S.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXII, 579 p. online resource.
  abstract: Variational analysis is a fruitful area in mathematics that, on the one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which enters naturally not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the heart of variational analysis and its applications. This monograph in two volumes contains a comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite dimensional spaces and presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first of volume is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume contains various applications. Both volumes contain abundant bibliographies and extensive commentaries. This book will be of interest to researchers and graduate students in mathematical sciences. It may also be useful to a broad range of researchers, practitioners, and graduate students involved in the study and applications of variational methods in economics, engineering, control systems, operations research, statistics, mechanics, and other applied sciences.
  table of contents: Generalized Differentiation in Banach Spaces: Generalized Normals to Nonconvex Sets. Coderivatives of Set-Valued Mappings. Subdifferentials of Nonsmooth Functions -- Extremal Principle in Variational Analysis: Set Extremality and Nonconvex Separation. Extremal Principle in Asplund Spaces. Relations with Variational Principles. Representations and Characterizations in Asplund Spaces. Versions of the Extremal Principle in Banach Spaces -- Full Calculus in Asplund Spaces: Calculus Rules for Normals and Coderivatives. Subdifferential Calculus and Related Topics. SNC Calculus for Sets and Mappings -- Lipschitzian Stability and Sensivity Analysis: Neighborhood Criteria and Exact Bounds. Pointbased Characterizations. Sensitivity Analysis for Constraint Systems. Sensitivity Analysis for Variational Systems -- References -- Glossary of Notation -- Index of Statements.
  note: by Boris S. Mordukhovich.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Numerical analysis
  subject:
    topic: Calculus of variations
  subject:
    topic: Mathematics
  subject:
    topic: Calculus of Variations and Optimal Control; Optimization
  subject:
    topic: Global Analysis and Analysis on Manifolds
  subject:
    topic: Numerical Analysis
  subject:
    topic: Applications of Mathematics
  classification: QA315-316
  classification: QA402.3
  classification: QA402.5-QA402.6
  classification: 515.64
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 330
  identifier: 9783540312475
  identifier: http://dx.doi.org/10.1007/3-540-31247-1
  record info:
    record creation date: 100301
    record change date: 20151106091102.0
    record identifier: 978-3-540-31247-5