AuthorAuslender, Alfred. author
TitleAsymptotic Cones and Functions in Optimization and Variational Inequalities [electronic resource] / by Alfred Auslender, Marc Teboulle
ImprintNew York, NY : Springer New York, 2003
Connect tohttp://dx.doi.org/10.1007/b97594
Descript XII, 249 p. online resource

SUMMARY

Nonlinear applied analysis and in particular the related ?elds of continuous optimization and variational inequality problems have gone through major developments over the last three decades and have reached maturity. A pivotal role in these developments has been played by convex analysis, a rich area covering a broad range of problems in mathematical sciences and its applications. Separation of convex sets and the Legendre-Fenchel conjugate transforms are fundamental notions that have laid the ground for these fruitful developments. Two other fundamental notions that have contributed to making convex analysis a powerful analytical tool and that haveoftenbeenhiddeninthesedevelopmentsarethenotionsofasymptotic sets and functions. The purpose of this book is to provide a systematic and comprehensive account of asymptotic sets and functions, from which a broad and u- ful theory emerges in the areas of optimization and variational inequa- ties. There is a variety of motivations that led mathematicians to study questions revolving around attaintment of the in?mum in a minimization problem and its stability, duality and minmax theorems, convexi?cation of sets and functions, and maximal monotone maps. In all these topics we are faced with the central problem of handling unbounded situations


CONTENT

Convex Analysis and Set-Valued Maps: A Review -- Asymptotic Cones and Functions -- Existence and Stability in Optimization Problems -- Minimizing and Stationary Sequences -- Duality in Optimization Problems -- Maximal Monotone Maps and Variational Inequalities


SUBJECT

  1. Mathematics
  2. Mathematical analysis
  3. Analysis (Mathematics)
  4. Potential theory (Mathematics)
  5. Mathematical models
  6. Mathematical optimization
  7. Calculus of variations
  8. Operations research
  9. Management science
  10. Mathematics
  11. Mathematical Modeling and Industrial Mathematics
  12. Analysis
  13. Potential Theory
  14. Calculus of Variations and Optimal Control; Optimization
  15. Optimization
  16. Operations Research
  17. Management Science