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Lecture Notes in Economics and Mathematical Systems

# Infinite Programming

## Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984

Editors: Anderson, Edward J., Philpott, Andrew B. (Eds.)

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Infinite programming may be defined as the study of mathematical programming problems in which the number of variables and the number of constraints are both possibly infinite. Many optimization problems in engineering, operations research, and economics have natural formul- ions as infinite programs. For example, the problem of Chebyshev approximation can be posed as a linear program with an infinite number of constraints. Formally, given continuous functions f,gl,g2, ••• ,gn on the interval [a,b], we can find the linear combination of the functions gl,g2, ... ,gn which is the best uniform approximation to f by choosing real numbers a,xl,x2, •.. ,x to n minimize a t€ [a,b]. This is an example of a semi-infinite program; the number of variables is finite and the number of constraints is infinite. An example of an infinite program in which the number of constraints and the number of variables are both infinite, is the well-known continuous linear program which can be formulated as follows. T minimize ~ c(t)Tx(t)dt t b(t) , subject to Bx(t) + fo Kx(s)ds x(t) .. 0, t € [0, T] • If x is regarded as a member of some infinite-dimensional vector space of functions, then this problem is a linear program posed over that space. Observe that if the constraint equations are differentiated, then this problem takes the form of a linear optimal control problem with state IV variable inequality constraints.

• Openness, Closedness and Duality in Banach Spaces with Applications to Continuous Linear Programming

Pages 1-15

Pomerol, J. Ch.

• Conditions for the Closedness of the Characteristic Cone Associated with an Infinite Linear System

Pages 16-28

Goberna, M. A. (et al.)

• Symmetric Duality: A Prelude

Pages 29-36

Karney, D. F.

• Algebraic fundamentals of linear programming

Pages 37-52

Nash, Peter

• On Regular Semi-Infinite Optimization

Pages 53-64

Jongen, H. Th. (et al.)

### Buy this book

eBook $109.00 price for USA in USD (gross) • ISBN 978-3-642-46564-2 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Softcover$139.00
price for USA in USD
• ISBN 978-3-540-15996-4
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.

## Bibliographic Information

Bibliographic Information
Book Title
Infinite Programming
Book Subtitle
Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984
Editors
• Edward J. Anderson
• Andrew B. Philpott
Series Title
Lecture Notes in Economics and Mathematical Systems
Series Volume
259
1985
Publisher
Springer-Verlag Berlin Heidelberg
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-46564-2
DOI
10.1007/978-3-642-46564-2
Softcover ISBN
978-3-540-15996-4
Series ISSN
0075-8442
Edition Number
1
Number of Pages
XIV, 248
Topics