Variational Calculus and Optimal Control

by Troutman, John L.

• ISBN13: 9780387945118
• ISBN10: 0387945113
• Edition: 2nd
• Format: Hardcover
• Copyright: 1996-01-01
• Publisher: Springer Verlag

Summary

The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science.

Table of Contents

Preface
Review of Optimization in R[superscript d]	p. 1
Standard Optimization Problems	p. 13
Linear Spaces and Gateaux Variations	p. 36
Minimization of Convex Functions	p. 53
The Lemmas of Lagrange and Du Bois-Reymond	p. 97
Local Extrema in Normed Linear Spaces	p. 103
The Euler-Lagrange Equations	p. 145
Piecewise C[superscript 1] Extremal Functions	p. 197
Variational Principles in Mechanics	p. 234
Sufficient Conditions for a Minimum	p. 282
Control Problems and Sufficiency Considerations	p. 341
Necessary Conditions for Optimality	p. 378
App. A.0. Compact Sets in R[superscript d]	p. 419
App. A.1. The Intermediate and Mean Value Theorems	p. 421
App. A.2. The Fundamental Theorem of Calculus	p. 423
App. A.3. Partial Integrals: Leibniz' Formula	p. 425
App. A.4. An Open Mapping Theorem	p. 427
App. A.5. Families of Solutions to a System of Differential Equations	p. 429
App. A.6. The Rayleigh Ratio	p. 435
App. A.7. Linear Functionals and Tangent Cones in R[superscript d]	p. 441
Bibliography	p. 445
Historical References	p. 450
Answers to Selected Problems	p. 452
Index	p. 457
Table of Contents provided by Blackwell. All Rights Reserved.