Variational Methods in Optimization

Be the first to write a review

All Available Formats + Editions

$5.95

——

Paperback

$5.95

——

Variational Methods in Optimization Pub. Date: 6/19/1998 Publisher: Dover Publications
$4.83

——

Hardcover

$4.83

——

Variational Methods in Optimization Pub. Date: 1/28/1974 Publisher: Prentice Hall

Want to read this on your NOOK? Request as NOOK Book from the publisher

Thank you for requesting this book as a NOOK book from the publisher.

Customers Who Bought This Also Bought

Advertising

Overview

Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. Clear, well-illustrated treatment addresses optimization problems in a diverse array of fields. Only basic knowledge of calculus required. 1974 edition.

Editorial Reviews

Booknews

Gives an elementary exposition of an extension of the standard differentiation method which leads to an increase in both the number and type of problems that can be solved. Covers problems with fixed endpoints, variable endpoints, isoperimetric constraints, global inequality constraints, the inverse function theorem, and the chain rule of differentiation. Intended for use as a stand-alone text or as a supplement to courses in applied economics, the calculus of variations, optimal control theory, or terminal calculus. An unabridged republication of the work originally published in 1974 by Prentice-Hall, Inc. Annotation c. by Book News, Inc., Portland, Or.

Product Details

ISBN-13: 9780486404554
Publisher: Dover Publications
Publication date: 6/19/1998
Pages: 394
Series: Dover Books on Mathematics Series
Product dimensions: 5.61 (w) x 8.19 (h) x 0.75 (d)

1. Functionals
1.1 Introduction; Examples of Optimizational Problems
1.2 Vector Spaces
1.3 Functionals
1.4 Normed Vector Spaces
1.5 Continuous Functionals
1.6 Linear Functionals
2. A Fundamental Necessary Condition for an Extremum
2.1 Introduction
2.2 A Fundamental Necessary Condition for an Extremum
2.3 Some Remarks on the Gâteaux Variation
2.4 Examples on the Calculation of Gâteaux Variations
2.5 An Optimization Problem in Production Planning
2.6 Some Remarks on the Fréchet Differential
3. The Euler-Lagrange Necessary Condition for an Extremum with Constraints
3.1 Extremum Problems with a Single Constraint
3.2 Weak Continuity of Variations
3.3 Statement of the Euler-Lagrange Multiplier Theorem for a Single Constraint
3.4 Three Examples, and Some Remarks on the Geometrical Significance of the Multiplier Theorem
3.5 Proof of the Euler-Lagrange Multiplier Theorem
3.6 The Euler-Lagrange Multiplier Theorem for Many Constraints
3.7 An Optimum Consumption Policy with Terminal Savings Constraint During a Period of Inflation
3.8 The Meaning of the Euler-Lagrange Multipliers
3.9 Chaplygin's Problem, or a Modern Version of Queen Dido's Problem
3.10 The John Multiplier Theorem
4. Applications of the Euler-Lagrange Multiplier Theorem in the Calculus of Variations
4.1 Problems with Fixed End Points
4.2 John Bernoulli's Brachistochrone Problem, and Brachistochrones Through the Earth
4.3 Geodesic Curves
4.4 Problems with Variable End Points
4.5 How to Design a Thrilling Chute-the-Chute
4.6 Functionals Involving Several Unknown Functions
4.7 Fermat's Principle in Geometrical Optics
4.8 Hamilton's Principle of Stationary Action; an Example on Small Vibrations
4.9 The McShane-Blankinship Curtain Rod Problem; Functionals Involving Higher-Order Derivatives
4.10 Functionals Involving Several Independent Variables; the Minimal Surface Problem
4.11 The Vibrating String
5. Applications of the Euler-Lagrange Multiplier Theorem to Problems with Global Pointwise Inequality Constraints
5.1 Slack Functions and Composite Curves
5.2 An Optimum Consumption Policy with Terminal Savings Constraint Without Extreme Hardship
5.3 A Problem in Production Planning with Inequality Constraints
6. Applications of the Euler-Lagrange Multiplier Theorem in Elementary Control Theory
6.1 Introduction
6.2 A Rocket Control Problem: Minimum Time
6.3 A Rocket Control Problem: Minimum Fuel
6.4 A More General Control Problem
6.5 A Simple Bang-Bang Problem
6.6 Some Remarks on the Maximum Principle and Dynamic Programming
7. The Variational Description of Sturm-Liouville Eigenvalues
7.1 Introduction to Sturm-Liouville Problems
7.2 The Relation Between the Lowest Eigenvalue and the Rayleigh Quotient
7.3 The Rayleigh-Ritz Method for the Lowest Eigenvalue
7.4 Higher Eigenvalues and the Rayleigh Quotient
7.5 The Courant Minimax Principle
7.6 Some Implications of the Courant Minimax Principle
7.7 Further Extensions of the Theory
7.8 Some General Remarks on the Ritz Method of Approximate Minimization
8. Some Remarks on the Use of the Second Variation in Extremum Problems
8.1 Higher-Order Variations
8.2 A Necessary Condition Involving the Second Variation at an Extremum
8.3 Sufficient Conditions for a Local Extremum Appendix 1. The Cauchy and Schwarz Inequalities Appendix 2. An Example on Normed Vector Spaces Appendix 3. An Integral Inequality Appendix 4. A Fundamental Lemma of the Calculus of Variations Appendix 5. Du Bois-Reymond's Derivation of the Euler-Lagrange Equation Appendix 6. A Useful Result from Calculus Appendix 7. The Construction of a Certain Function Appendix 8. The Fundamental Lemma for the Case of Several Independent Variables Appendix 9. The Kinetic Energy for a Certain Model of an Elastic String Appendix 10. The Variation of an Initial Value Problem with Respect to a Parameter
Subject Index; Author Index

Customer Reviews

Be the first to write a review

( 0 )

Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Review Guidelines

Tell the world what you think of this product.

Add Recommendations

Your Name: Create a Pen Name or Leave Anonymously

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

- HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
- Time-sensitive information such as tour dates, signings, lectures, etc.
- Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
- Comments focusing on the author or that may ruin the ending for others
- Phone numbers, addresses, URLs
- Pricing and availability information or alternative ordering information
- Advertisements or commercial solicitation

Reminder:

- By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
- Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
- See Terms of Use for other conditions and disclaimers.

If you find inappropriate content, please report it to Barnes & Noble

Variational Methods in Optimization

Overview

All Available Formats + Editions

Customers Who Bought This Also Bought

More About This Book

Overview

Related Subjects

Editorial Reviews

Booknews

Product Details

Table of Contents

Customer Reviews

Rating Distribution

5 Star

4 Star

3 Star

2 Star

1 Star

Your Rating:

Your Recommendations:

Barnes & Noble.com Review Rules

Reviews by Our Customers Under the Age of 13

What to exclude from your review:

Reviews should not contain any of the following:

Reminder:

Recommend other products that relate to your review. Just search for them below and share!