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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Variational Analysis and Set Optimization - Developments and Applications in Decision Making (Hardcover)
Loot Price: R4,731
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Variational Analysis and Set Optimization - Developments and Applications in Decision Making (Hardcover)
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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.
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