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Operational research. Game theory --- Mathematical optimization --- 519.6 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space.

Monotone operators. --- Monotonic functions. --- Banach spaces. --- Opérateurs monotones --- Fonctions monotones --- Banach, Espaces de --- Monotone operators --- Monotonic functions --- Banach spaces --- Duality theory (Mathematics) --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Maxima and minima. --- Opérateurs monotones --- EPUB-LIV-FT SPRINGER-B --- Functions, Monotonic --- Minima --- Mathematics. --- Functional analysis. --- Operator theory. --- Calculus of variations. --- Functional Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Operator Theory. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Functions of real variables --- Operator theory --- Algebra --- Mathematical analysis --- Topology --- Functions of complex variables --- Generalized spaces --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis

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The symposium Operations Research 2007 was held from September 5-7, 2007 at the Saarland University in Saarbru ¨cken. This international conference is at the same time the annual meeting of the German - erations Research Society (GOR). The transition in Germany (and many other countries in Europe) from a production orientation to a service society combined with a continuous demographic change generated a need for intensi?ed Op- ations Research activities in this area. On that account this conference has been devoted to the role of Operations Research in the service industry. The links to Operations Research are manifold and include many di?erent topics which are particularly emphasized in scienti?c sections of OR 2007. More than 420 participants from 30 countries made this event very international and successful. The program consisted of three p- nary,elevensemi-plenaryandmorethan300contributedpresentations, which had been organized in 18 sections. During the conference, the GOR Dissertation and Diploma Prizes were awarded. We congratulate all winners, especially Professor Wolfgang Domschke from the Da- stadt University of Technology, on receiving the GOR Scienti?c Prize Award.

Operations research --- Operations research. --- Mathematical optimization. --- Operations Research/Decision Theory. --- Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Simulation methods --- System analysis --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making

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This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers.

Stochastic processes. --- Mathematical optimization. --- Risk assessment --- Portfolio management --- Mathematical models. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Random processes --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Probabilities --- Stochastic processes --- Mathematical optimization --- Mathematical models --- E-books --- Investment management

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Optimization has become an essential tool in addressing the limitation of resources and need for better decision-making in the medical field. Both continuous and discrete mathematical techniques are playing an increasingly important role in understanding several fundamental problems in medicine. This volume presents a wide range of medical applications that can utilize mathematical computing. Examples include using an algorithm for considering the seed reconstruction problem in brachytherapy and using optimization-classification models to assist in the early prediction, diagnosis and detection of diseases. Discrete optimization techniques and measures derived from the theory of nonlinear dynamics, with analysis of multi-electrode electroencephalographic (EEG) data, assist in predicting impending epileptic seizures. Mathematics in medicine can also be found in recent cancer research. Sophisticated mathematical models and optimization algorithms have been used to generate treatment plans for radionuclide implant and external beam radiation therapy. Optimization techniques have also been used to automate the planning process in Gamma Knife treatment, as well as to address a variety of medical image registration problems. This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization.

Medicine --- Mathematical optimization. --- Mathematics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Medical mathematics --- Medicine. --- Radiology, Medical. --- Medicine/Public Health, general. --- Optimization. --- Calculus of Variations and Optimal Control; Optimization. --- Imaging / Radiology. --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics --- Clinical sciences --- Medical profession --- Human biology --- Life sciences --- Medical sciences --- Pathology --- Physicians --- Health Workforce --- Calculus of variations. --- Radiology. --- Radiological physics --- Physics --- Radiation --- Isoperimetrical problems --- Variations, Calculus of