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This book serves as an introductory text to optimization theory in normed spaces. Topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook 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.

Mathematical optimization. --- Nonlinear theories. --- Optimisation mathématique --- Théories non linéaires --- Mathematical optimization --- Nonlinear theories --- Operations Research --- Calculus --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Nonlinear problems --- Nonlinearity (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematics. --- Operations research. --- Decision making. --- Calculus of variations. --- Computational intelligence. --- Calculus of Variations and Optimal Control; Optimization. --- Operation Research/Decision Theory. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Math --- Science --- Decision making --- Engineering. --- Operations Research/Decision Theory. --- Construction --- Industrial arts --- Technology --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis

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This book presents fundamentals and important results of vector optimization in a general setting. 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.

Linear topological spaces. --- Mathematical optimization. --- Vector spaces. --- Management --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Business & Economics --- Management Theory --- Operations Research --- Vector valued functions. --- Functions, Vector --- Functions, Vector valued --- Business. --- Operations research. --- Decision making. --- Management science. --- Business and Management. --- Operation Research/Decision Theory. --- Optimization. --- Operations Research, Management Science. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functional analysis --- Functions of real variables

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