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 semiinfinite 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 wellknown 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 infinitedimensional 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.
 Table of contents (18 chapters)


Openness, Closedness and Duality in Banach Spaces with Applications to Continuous Linear Programming
Pages 115

Conditions for the Closedness of the Characteristic Cone Associated with an Infinite Linear System
Pages 1628

Symmetric Duality: A Prelude
Pages 2936

Algebraic fundamentals of linear programming
Pages 3752

On Regular SemiInfinite Optimization
Pages 5364

Table of contents (18 chapters)
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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
 Copyright
 1985
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783642465642
 DOI
 10.1007/9783642465642
 Softcover ISBN
 9783540159964
 Series ISSN
 00758442
 Edition Number
 1
 Number of Pages
 XIV, 248
 Topics