Buch, Englisch, 765 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 12941 g
Reihe: Vector Optimization
An Introduction with Applications
Buch, Englisch, 765 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 12941 g
Reihe: Vector Optimization
ISBN: 978-3-642-54264-0
Verlag: Springer
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 economicsamong other things.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.