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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