Set-valued Optimization (eBook)

An Introduction with Applications

Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu (Autoren)

eBook Download: PDF

2014 | 2015
XXII, 765 Seiten
Springer Berlin (Verlag)
978-3-642-54265-7 (ISBN)

Infos

Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economics among other things.

Inhalt

Introduction.- Order Relations and Ordering Cones.- Continuity and Differentiability.- Tangent Cones and Tangent Sets.- Nonconvex Separation Theorems.- Hahn-Banach Type Theorems.- Hahn-Banach Type Theorems.- Conjugates and Subdifferentials.- Duality.- Existence Results for Minimal Points.- Ekeland Variational Principle.- Derivatives and Epiderivatives of Set-valued Maps.- Optimality Conditions in Set-valued Optimization.- Sensitivity Analysis in Set-valued Optimization and Vector Variational Inequalities.- Numerical Methods for Solving Set-valued Optimization Problems.- Applications.

Produkt-Details

• Erscheint lt. Verlag: 20.10.2014
• Reihe/Serie: Vector Optimization
• Reihe/Serie: Vector Optimization
• Zusatzinfo: XXII, 765 p. 29 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Schlagworte: cone properties • existence theorem • Hahn-Banach extension • minimal point • nonconvex separation • variational analysis
• ISBN-10: 3-642-54265-4 / 3642542654
• ISBN-13: 978-3-642-54265-7 / 9783642542657