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Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where" optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.

Urban transportation --- Traffic estimation --- Mathematical optimization --- Transportation Economics --- Business & Economics --- Mathematical models --- Transportation --- Mathematical optimization. --- Mathematical models. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Public transportation --- Transport --- Transportation, Primitive --- Transportation companies --- Transportation industry --- Economic aspects --- Mathematics. --- Calculus of variations. --- Operations research. --- Management science. --- Manifolds (Mathematics). --- Complex manifolds. --- Calculus of Variations and Optimal Control; Optimization. --- Operations Research, Management Science. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Math --- Science --- Mathematical analysis --- Simulation methods --- System analysis --- Locomotion --- Commerce --- Communication and traffic --- Storage and moving trade --- Cell aggregation --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation

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Functional analysis --- Partial differential equations --- Operational research. Game theory --- Mathematics --- Computer. Automation --- differentiaalvergelijkingen --- toegepaste wiskunde --- functies (wiskunde) --- automatisering --- wiskunde --- kansrekening

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Mathematical analysis --- Mathematics --- Fluid mechanics --- Materials sciences --- Engineering sciences. Technology --- Production management --- Computer. Automation --- analyse (wiskunde) --- toegepaste wiskunde --- DFMA (design for manufacture and assembly) --- ingenieurswetenschappen --- mechanica --- numerieke analyse

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The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems. Key topics and features: * Presents foundational introduction to shape optimization theory * Studies certain classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, and optimization problems over classes of convex domains * Treats optimal control problems under a general scheme, giving a topological framework, a survey of "gamma"-convergence, and problems governed by ODE * Examines shape optimization problems with Dirichlet and Neumann conditions on the free boundary, along with the existence of classical solutions * Studies optimization problems for obstacles and eigenvalues of elliptic operators * Poses several open problems for further research * Substantial bibliography and index Driven by good examples and illustrations and requiring only a standard knowledge in the calculus of variations, differential equations, and functional analysis, the book can serve as a text for a graduate course in computational methods of optimal design and optimization, as well as an excellent reference for applied mathematicians addressing functional shape optimization problems.

Computer. Automation --- automatisering --- toegepaste wiskunde --- Functional analysis --- Mathematics --- differentiaalvergelijkingen --- kansrekening --- wiskunde --- Operational research. Game theory --- Partial differential equations --- functies (wiskunde) --- Mathematical optimization --- Shapes --- Optimisation mathématique --- Formes --- EPUB-LIV-FT SPRINGER-B LIVMATHE --- Mathematical optimization. --- Shapes. --- Differential equations, partial. --- Functional analysis. --- Functional equations. --- Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization. --- Partial Differential Equations. --- Functional Analysis. --- Difference and Functional Equations. --- Applications of Mathematics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science --- Equations, Functional --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Calculus of variations. --- Partial differential equations. --- Difference equations. --- Applied mathematics. --- Engineering mathematics. --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Isoperimetrical problems --- Variations, Calculus of --- Engineering --- Engineering analysis