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Ongoing global changes bring fundamentally new scientific problems requiring new concepts and tools. A key issue concerns a vast variety of practically irreducible uncertainties, which challenge our traditional models and require new concepts and analytical tools. The uncertainty critically dominantes, e.g., the climate change debates. In short, the dilemma is concerned with enormous costs vs. massive uncertainties of potential extreme impacts. Traditional scientific approaches usually rely on real observations and experiments. Yet no sufficient observations exist for new problems, and "pure" experiments and learning by doing may be very expensive, dangerous, or simply impossible. In addition, available historical observations are contaminated by actions, policies. The complexity of new problems does not allow to achieve enough certainty by increasing the resolution of models or by bringing in more links. Hence, new tools for modeling and management of uncertainty are needed, as given in this book.

Operations research. --- Decision making. --- Mathematics. --- Mathematical optimization. --- Computational intelligence. --- Economics. --- Management science. --- Economics, general. --- Mathematics, general. --- Operation Research/Decision Theory. --- Optimization. --- Computational Intelligence. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Economic theory --- Political economy --- Social sciences --- Economic man --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Simulation methods --- System analysis --- Math --- Science --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making --- Uncertainty --- Stochastic processes --- Mathematical models --- Reasoning --- Engineering. --- Operations Research/Decision Theory. --- Construction --- Industrial arts --- Technology

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Stochastic processes

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German literature --- Switzerland --- Suisse --- Description and travel --- Descriptions et voyages

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This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.

Economics/Management Science. --- Operation Research/Decision Theory. --- Optimization. --- Computational Intelligence. --- Economics. --- Mathematical optimization. --- Engineering. --- Operations research. --- Economie politique --- Optimisation mathématique --- Ingénierie --- Recherche opérationnelle --- Stochastic processes. --- Management --- Business & Economics --- Management Theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Random processes --- Business. --- Decision making. --- Computational intelligence. --- Business and Management. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Trade --- Economics --- Commerce --- Industrial management --- Decision making --- Probabilities --- Operations Research/Decision Theory. --- Construction --- Industrial arts --- Technology

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Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Stochastic processes. --- Mathematical optimization. --- Processus stochastiques --- Optimisation mathématique --- Stochastic processes --- Mathematical optimization --- Management Theory --- Operations Research --- Applied Mathematics --- Civil & Environmental Engineering --- Management --- Engineering & Applied Sciences --- Business & Economics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Random processes --- Business. --- Operations research. --- Decision making. --- Computational intelligence. --- Business and Management. --- Operation Research/Decision Theory. --- Optimization. --- Computational Intelligence. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Trade --- Economics --- Commerce --- Industrial management --- Decision making --- Probabilities --- Engineering. --- Operations Research/Decision Theory. --- Construction --- Industrial arts --- Technology