Optimization—Theory and Applications Problems with Ordinary Differential Equations
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...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1983, 1983
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| Edition: | 1st ed. 1983 |
| Series: | Stochastic Modelling and Applied Probability
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| Subjects: | |
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| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Problems of Optimization—A General View
- 2 The Classical Problems of the Calculus of Variations: Necessary Conditions and Sufficient Conditions; Convexity and Lower Semicontinuity
- 3 Examples and Exercises on Classical Problems
- 4 Statement of the Necessary Condition for Mayer Problems of Optimal Control
- 5 Lagrange and Bolza Problems of Optimal Control and Other Problems
- 6 Examples and Exercises on Optimal Control
- 7 Proofs of the Necessary Condition for Control Problems and Related Topics
- 8 The Implicit Function Theorem and the Elementary Closure Theorem
- 9 Existence Theorems: The Bounded, or Elementary, Case
- 10 Closure and Lower Closure Theorems under Weak Convergence
- 11 Existence Theorems: Weak Convergence and Growth Conditions
- 12 Existence Theorems: The Case of an Exceptional Set of No Growth
- 13 Existence Theorems: The Use of Lipschitz and Tempered Growth Conditions
- 14 Existence Theorems: Problems of Slow Growth
- 15 Existence Theorems: The Use of Mere Pointwise Convergence on the Trajectories
- 16 Existence Theorems: Problems with No Convexity Assumptions
- 17 Duality and Upper Semicontinuity of Set Valued Functions
- 18 Approximation of Usual and of Generalized Solutions
- Author Index