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E-bok
PDF, Engelska, 20121 672 kr
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This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.
Del 17 - Stochastic Modelling and Applied Probability
Optimization—Theory and Applications
Problems with Ordinary Differential Equations
Häftad, Engelska, 2011
1 416 kr
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This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.
979 kr
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Dynamical Systems compiles the lectures and contributed papers read at the International Symposium on Dynamical Systems held at the University of Florida in Gainesville, Florida on March 24-26, 1976. This book discusses the principle of exchange of stability; weak-invariance and rest points in control systems; local controllability in nonlinear systems; and unitary treatment of various types of systems in stability-theory. The optimization of structural geometry; dispersal manifolds in partial differential games; remarks on existence theorems for Pareto optimality; and stability of solutions bifurcating from steady or periodic solutions are also elaborated. This compilation likewise covers the linear neutral functional differential equations on a Banach space; radiation reaction in electrodynamics; and buckling of cylindrical shells with small curvature. This publication is beneficial to students and researchers working on dynamical systems.