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Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.

Locally convex spaces. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Spaces, Locally convex --- Linear topological spaces

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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