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

Paperback(Softcover reprint of the original 1st ed. 1985)

\$139.00
• Want it by Monday, October 1?   Order by 12:00 PM Eastern and choose Expedited Shipping at checkout.

Overview

Infinite Programming: Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7-10, 1984 by Edward J. Anderson

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.

Product Details

ISBN-13: 9783540159964 Springer Berlin Heidelberg 12/06/1985 Lecture Notes in Economics and Mathematical Systems , #259 Softcover reprint of the original 1st ed. 1985 248 6.69(w) x 9.61(h) x 0.02(d)