Variable Ordering Structures in Vector Optimization

• Main Author: Eichfelder, Gabriele (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.
• Series: Vector Optimization,
• Subjects: Mathematics.; Operations research.; Decision making.; Applied mathematics.; Engineering mathematics.; Mathematical optimization.; Optimization.; Operation Research/Decision Theory.; Applications of Mathematics.; Continuous Optimization.

This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by...

Table of Contents:

• 1 Variable ordering structures
• 2 Optimality concepts and their characterization
• 3 Properties of cone-valued maps
• 4 Linear scalarizations
• 5 Nonlinear scalarizations
• 6 Scalarization for variable orderings given by Bishop-Phelps cones
• 7 Optimality conditions
• 8 Duality results
• 9 Numerical methods
• 10 Outlook and further application areas.