Vector Optimization and Monotone Operators via Convex Duality
Recent Advances
1st Edition
Published on 3. September 2014
XVII, 269 pages
978-3-319-08900-3 (ISBN)
Description
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
XVII, 269 p.
File size
2,75 MB
ISBN-13
978-3-319-08900-3 (9783319089003)
DOI
10.1007/978-3-319-08900-3
Schweitzer Classification
Other editions
Additional editions
Book
09/2014
Springer
€128.39
Shipment within 10-15 days
Person
Sorin-Mihai Grad is currently working within the Faculty of Mathematics of Chemnitz University of Technology, Germany, where he achieved his PhD in 2006 and his Habilitation in 2014. He is co-author of the book "Duality in Vector Optimization" (Springer, 2009).
Content
Introduction and preliminaries.- Duality for scalar optimization problems.- Minimality concepts for sets.- Vector duality via scalarization for vector optimization problems.- General Wolfe and Mond-Weir duality.- Vector duality for linear and semidefinite vector optimization problems.- Monotone operators approached via convex Analysis.
