Variational Calculus and Optimal Control

Optimization with Elementary Convexity

John L. Troutman

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English

Springer-Verlag New York Inc.
01 December 1995

Calculus of variations; Euclidean geometry

Series: Undergraduate Texts in Mathematics

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.

By: John L. Troutman
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: 2nd ed. 1996
Dimensions: Height: 235mm, Width: 155mm, Spine: 26mm
Weight: 1.880kg
ISBN: 9780387945118
ISBN 10: 0387945113
Series: Undergraduate Texts in Mathematics
Pages: 462
Publication Date: 01 December 1995
Audience: College/higher education , A / AS level
Format: Hardback
Publisher's Status: Active

0 Review of Optimization in ?d.- Problems.- One Basic Theory.- 1 Standard Optimization Problems.- 2 Linear Spaces and Gâteaux Variations.- 3 Minimization of Convex Functions.- 4 The Lemmas of Lagrange and Du Bois-Reymond.- 5 Local Extrema in Normed Linear Spaces.- 6 The Euler-Lagrange Equations.- Two Advanced Topics.- 7 Piecewise C1 Extremal Functions.- 8 Variational Principles in Mechanics.- 9 Sufficient Conditions for a Minimum.- Three Optimal Control.- 10 Control Problems and Sufficiency Considerations.- 11 Necessary Conditions for Optimality.- A.1. The Intermediate and Mean Value Theorems.- A.2. The Fundamental Theorem of Calculus.- A.3. Partial Integrals: Leibniz’ Formula.- A.4. An Open Mapping Theorem.- A.5. Families of Solutions to a System of Differential Equations.- A.6. The Rayleigh Ratio.- Historical References.- Answers to Selected Problems.