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This book serves as an introductory text to optimization theory in
normed spaces and covers all areas of nonlinear optimization. It
presents fundamentals with particular emphasis on the application
to problems in the calculus of variations, approximation and
optimal control theory. The reader is expected to have a basic
knowledge of linear functional analysis.
Fundamentals and important results of vector optimization in a
general setting are presented in this book. The theory developed
includes scalarization, existence theorems, a generalized Lagrange
multiplier rule and duality results. Applications to vector
approximation, cooperative game theory and multiobjective
optimization are described. The theory is extended to set
optimization with particular emphasis on contingent epiderivatives,
subgradients and optimality conditions. Background material of
convex analysis being necessary is concisely summarized at the
beginning.
This second edition contains new parts on the adaptive
Eichfelder-Polak method, a concrete application to magnetic
resonance systems in medical engineering and additional remarks on
the contribution of F.Y. Edgeworth and V. Pareto. The bibliography
is updated and includes more recent important publications.
This book serves as an introductory text to optimization theory in
normed spaces and covers all areas of nonlinear optimization. It
presents fundamentals with particular emphasis on the application
to problems in the calculus of variations, approximation and
optimal control theory. The reader is expected to have a basic
knowledge of linear functional analysis.
In vector optimization one investigates optimization problems in an
abstract setting which have a not necessarily real-valued objective
function. This scientific discipline is closely related to
multi-objective optimization and multi-criteria decision making.
This book contains refereed contributions to the "International
Conference on Vector Optimization" held at the Technical University
of Darmstadt from August 4-7, 1986. This meeting was an
interdisciplinary forum devoted to new results in the theory, to
applications as well as to the solution of vector optimization
problems which are relevant in practice. Because of the great
variety of topics covered by the contributions, the 25 articles of
this volume are organized in different sections: Historical
retrospect, mathematical theory, goal setting and decision making,
engineering applications, and related topics. The papers of the
invited State-of-the-Art Tutorials given by Professors J.M.
Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.
This book serves as an introductory text to optimization theory in
normed spaces and covers all areas of nonlinear optimization. It
presents fundamentals with particular emphasis on the application
to problems in the calculus of variations, approximation and
optimal control theory. The reader is expected to have a basic
knowledge of linear functional analysis.
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