Set-valued Optimization
An Introduction with Applications
Business & Finance, Management & Leadership, Operations Research, Nonfiction, Science & Nature, Mathematics, Applied
| Author: | Christiane Tammer, Akhtar A. Khan, Constantin Zălinescu | ISBN: | 9783642542657 |
| Publisher: | Springer Berlin Heidelberg | Publication: | October 20, 2014 |
| Imprint: | Springer | Language: | English |
| Author: | Christiane Tammer, Akhtar A. Khan, Constantin Zălinescu |
| ISBN: | 9783642542657 |
| Publisher: | Springer Berlin Heidelberg |
| Publication: | October 20, 2014 |
| Imprint: | Springer |
| Language: | English |
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 economics among other things.
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 economics among other things.
