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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.
In mathematical modeling of processes one often encounters optimization problems involving more than one objective function, so that Multiobjective Optimization (or Vector Optimization) has received new impetus. The growing interest in multiobjective problems, both from the theoretical point of view and as it concerns applications to real problems, asks for a general scheme which embraces several existing developments and stimulates new ones. In this book the authors provide the newest results and applications of this quickly growing field. This book will be of interest to graduate students in mathematics, economics, and engineering, as well as researchers in pure and applied mathematics, economics, engineering, geography, and town planning. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book.
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.
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