Vector Optimization with Infimum and Supremum

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.

Summary

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.

Product details

• Authors: Andreas Löhne
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 06.06.2013
• EAN: 9783642268410
• ISBN: 978-3-642-26841-0
• No. of pages: 206
• Dimensions: 155 mm x 13 mm x 236 mm
• Weight: 336 g
• Illustrations: X, 206 p.
• Series: Vector Optimization; Vector Optimization
• Subjects: Social sciences, law, business > Business > General, dictionaries; Algebra, Operations Research, C, Algorithms, Optimization, Business and Management, Operations Research/Decision Theory, Operations Research and Decision Theory, Management & management techniques, Operations Research, Management Science, Management decision making, Management science, Numerical analysis, Operational research, Decision Making, Mathematical optimization, Order, Lattices, Ordered Algebraic Structures, Ordered algebraic structures