Relaxation in optimization theory and variational calculus

Author(s)

• Roubíček, Tomáš

Bibliographic Information

Relaxation in optimization theory and variational calculus

Tomáš Roubiček

（De Gruyter series in nonlinear analysis and applications, 4）

Walter de Gruyter, 1997

Note

Includes bibliographical references (p. [443]-462) and index (p. [469]-474)

Description and Table of Contents

Description

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jurgen Appell, Wurzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Torun, Poland Vicentiu D. Radulescu, Krakow, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jurgen Appell. Titles in planning include Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Table of Contents

• Background generalities: order and topology
• linear and convex analysis
• optimization theory
• functions and measure spaces
• means of continuous functions
• some differential and integral equations
• non-cooperative game theory. Theory of convex compactifications: convex compactifications
• canonical form of convex compactifications
• approximation of convex compactifications
• extension of mappings. Young measures and their generalizations: classical Young measures
• various generalizations
• approximation theory
• extensions of Nemytskii mappings. Relaxation in optimization theory: abstract optimization problems
• optimization problems on Lebesgue spaces
• example - optimal control of dynamical systems
• example - elliptic optimal control problems
• example - parabolic optimal control problems
• example - optimal control of integral equations. relaxation in variational calculus I: convex compactifications of Sobolev spaces
• relaxation of variational problems - p > 1
• optimality conditions for relaxed problems
• relaxation of variational problems - p = 1
• convex approximation of relaxed problems. relaxation in variational calculus II: prerequisites around quasiconvexity
• gradient generalized Young functionals
• relaxation scheme and its FEM-approximation
• further approximation - an inner case
• further approximation - an outer case
• double-well problem - sample calculations. Relaxation in game theory: abstract game-theoretical problems
• games on Lebesgue spaces
• example - games with dynamical systems
• example - elliptic games
• bibliography
• list of symbols. (Part contents).

by "Nielsen BookData"

Details

• NCID: BA31785557
• ISBN:
  • 3110145421
• LCCN: 96031728
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; New York
• Pages/Volumes: xiv, 474 p.
• Size: 25 cm
• Classification:
  • LCC : QA297.55
  • DC20 : 515/.64
• Subject Headings:
  • LCSH : Relaxation methods (Mathematics)
  • LCSH : Mathematical optimization
  • LCSH : Calculus of variations
• Parent Bibliography ID:
  • BA18314589