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This monograph explores key principles in the modern theory of dynamic optimization, incorporating important advances in the field to provide a comprehensive, mathematically rigorous reference. Emphasis is placed on nonsmooth analytic techniques, and an in-depth treatment of necessary conditions, minimizer regularity, and global optimality conditions related to the Hamilton-Jacobi equation is given. New, streamlined proofs of fundamental theorems are incorporated throughout the text that eliminate earlier, cumbersome reductions and constructions. The first chapter offers an extended overview of dynamic optimization and its history that details the shortcomings of the elementary theory and demonstrates how a deeper analysis aims to overcome them. Aspects of dynamic programming well-matched to analytical techniques are considered in the final chapter, including characterization of extended-value functions associated with problems having endpoint and state constraints, inverse verification theorems, sensitivity relationships, and links to the maximum principle. This text will be a valuable resource for those seeking an understanding of dynamic optimization. The lucid exposition, insights into the field, and comprehensive coverage will benefit postgraduates, researchers, and professionals in system science, control engineering, optimization, and applied mathematics.

Mathematical optimization. --- Calculus of variations. --- Dynamical systems. --- System theory. --- Control theory. --- Calculus of Variations and Optimization. --- Dynamical Systems. --- Systems Theory, Control.

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Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.

Operations Research --- Calculus --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Control theory --- Geometry. --- Mathematical models. --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Calculus of variations. --- Control engineering. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Analysis. --- Applications of Mathematics. --- Control. --- Euclid's Elements --- Mathematical optimization. --- Systems theory. --- Global analysis (Mathematics). --- Control and Systems Theory. --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Systems, Theory of --- Systems science --- Isoperimetrical problems --- Variations, Calculus of --- Philosophy

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With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents:Part ISecond-order decomposition model for image processing: numerical experimentationOptimizing spatial and tonal data for PDE-based inpaintingImage registration using phase・amplitude separationRotation invariance in exemplar-based image inpaintingConvective regularization for optical flowA variational method for quantitative photoacoustic tomography with piecewise constant coefficientsOn optical flow models for variational motion estimationBilevel approaches for learning of variational imaging modelsPart IINon-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problemsThe Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controlsControllability of Keplerian motion with low-thrust control systemsHigher variational equation techniques for the integrability of homogeneous potentialsIntroduction to KAM theory with a view to celestial mechanicsInvariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometryTime-optimal control for a perturbed Brockett integratorTwist maps and Arnold diffusion for diffeomorphismsA Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part IIndex

Image processing --- Image analysis --- Analysis of images --- Image interpretation --- Photographs --- Forensic sciences --- Imaging systems --- Pictorial data processing --- Picture processing --- Processing, Image --- Optical data processing --- Mathematical models. --- Inspection