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Variable Ordering Structures in Vector Optimization

 Buch
Besorgungstitel | Lieferzeit:3-5 Tage I
ISBN-13:
9783642542824
Einband:
Buch
Seiten:
190
Autor:
Gabriele Eichfelder
Gewicht:
4321 g
Format:
245x162x17 mm
Serie:
Vector Optimization
Sprache:
Englisch
Beschreibung:

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.
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 a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.

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.
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 a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.
Autor: Gabriele Eichfelder
Gabriele Eichfelder is Professor for mathematical methods of Operations Research at Technical University of Ilmenau, Germany.
Autor: Gabriele Eichfelder
ISBN-13:: 9783642542824
ISBN: 3642542824
Verlag: Springer, Berlin
Gewicht: 4321g
Seiten: 190
Sprache: Englisch
Auflage 2014
Sonstiges: Buch, 245x162x17 mm, 41 SW-Abb.