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Is the first volume devoted entirely to stochastic inverse
problems. Includes survey articles which makes it self-contained.
Aimed at a diverse audience, including applied mathematicians,
engineers, economists, and professionals from academia. Includes
the most recent developments on the subject, which so far have only
been available in the research literature.
Features First book on uncertainty quantification in variational
inequalities emerging from various network, economic, and
engineering models. Completely self-contained and lucid in style
Aimed for a diverse audience including applied mathematicians,
engineers, economists, and professionals from academia Includes the
most recent developments on the subject which so far have only been
available in the research literature.
This book contains the latest advances in variational analysis and
set / vector optimization, including uncertain optimization,
optimal control and bilevel optimization. Recent developments
concerning scalarization techniques, necessary and sufficient
optimality conditions and duality statements are given. New
numerical methods for efficiently solving set optimization problems
are provided. Moreover, applications in economics, finance and risk
theory are discussed. Summary The objective of this book is to
present advances in different areas of variational analysis and set
optimization, especially uncertain optimization, optimal control
and bilevel optimization. Uncertain optimization problems will be
approached from both a stochastic as well as a robust point of
view. This leads to different interpretations of the solutions,
which widens the choices for a decision-maker given his
preferences. Recent developments regarding linear and nonlinear
scalarization techniques with solid and nonsolid ordering cones for
solving set optimization problems are discussed in this book. These
results are useful for deriving optimality conditions for set and
vector optimization problems. Consequently, necessary and
sufficient optimality conditions are presented within this book,
both in terms of scalarization as well as generalized derivatives.
Moreover, an overview of existing duality statements and new
duality assertions is given. The book also addresses the field of
variable domination structures in vector and set optimization.
Including variable ordering cones is especially important in
applications such as medical image registration with uncertainties.
This book covers a wide range of applications of set optimization.
These range from finance, investment, insurance, control theory,
economics to risk theory. As uncertain multi-objective
optimization, especially robust approaches, lead to set
optimization, one main focus of this book is uncertain
optimization. Important recent developments concerning numerical
methods for solving set optimization problems sufficiently fast are
main features of this book. These are illustrated by various
examples as well as easy-to-follow-steps in order to facilitate the
decision process for users. Simple techniques aimed at
practitioners working in the fields of mathematical programming,
finance and portfolio selection are presented. These will help in
the decision-making process, as well as give an overview of
nondominated solutions to choose from.
This book contains the latest advances in variational analysis and
set / vector optimization, including uncertain optimization,
optimal control and bilevel optimization. Recent developments
concerning scalarization techniques, necessary and sufficient
optimality conditions and duality statements are given. New
numerical methods for efficiently solving set optimization problems
are provided. Moreover, applications in economics, finance and risk
theory are discussed. Summary The objective of this book is to
present advances in different areas of variational analysis and set
optimization, especially uncertain optimization, optimal control
and bilevel optimization. Uncertain optimization problems will be
approached from both a stochastic as well as a robust point of
view. This leads to different interpretations of the solutions,
which widens the choices for a decision-maker given his
preferences. Recent developments regarding linear and nonlinear
scalarization techniques with solid and nonsolid ordering cones for
solving set optimization problems are discussed in this book. These
results are useful for deriving optimality conditions for set and
vector optimization problems. Consequently, necessary and
sufficient optimality conditions are presented within this book,
both in terms of scalarization as well as generalized derivatives.
Moreover, an overview of existing duality statements and new
duality assertions is given. The book also addresses the field of
variable domination structures in vector and set optimization.
Including variable ordering cones is especially important in
applications such as medical image registration with uncertainties.
This book covers a wide range of applications of set optimization.
These range from finance, investment, insurance, control theory,
economics to risk theory. As uncertain multi-objective
optimization, especially robust approaches, lead to set
optimization, one main focus of this book is uncertain
optimization. Important recent developments concerning numerical
methods for solving set optimization problems sufficiently fast are
main features of this book. These are illustrated by various
examples as well as easy-to-follow-steps in order to facilitate the
decision process for users. Simple techniques aimed at
practitioners working in the fields of mathematical programming,
finance and portfolio selection are presented. These will help in
the decision-making process, as well as give an overview of
nondominated solutions to choose from.
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.
The chapters in this volume, written by international experts
from different fields of mathematics, are devoted to honoring
George Isac, a renowned mathematician. These contributions focus on
recent developments in complementarity theory, variational
principles, stability theory of functional equations, nonsmooth
optimization, and several other important topics at the forefront
of nonlinear analysis and optimization.
The chapters in this volume, written by international experts
from different fields of mathematics, are devoted to honoring
George Isac, a renowned mathematician. These contributions focus on
recent developments in complementarity theory, variational
principles, stability theory of functional equations, nonsmooth
optimization, and several other important topics at the forefront
of nonlinear analysis and optimization.
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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