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approximating infinite linear programming problems
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diegotorquemada@yahoo.com
science forum beginner


Joined: 11 Oct 2005
Posts: 17

PostPosted: Mon Jul 17, 2006 10:29 am    Post subject: approximating infinite linear programming problems Reply with quote

Hello group!

I would like to ask about some reference about the following problem:
show that the solution of a infinte linear programming problem is the
limit of the solution of some sequence of finite linear programming
problems.

In a longer version, I would post my question like


I need to prove a theorem that shows that some sequence of linear
programming problems converges to a infinite linear programming
problem:

something like

If Prob_n: is
max (1/n) sum_{i=1}^n y(i)
s.t.
0 <= x(i) <= 2
0 <= y(i) <= 4
0 <= (1/n) \sum_{j=1}^i [x(j) - y(j)] <= 1

for all i= 1, 2, ..., n

then prob_n tends to prob^*

Prob^*
max \int_0^1 y(t) dt
s.t.
0 <= x(t) <= 2
0 <= y(t) <= 4
0 <= \int_0^t x(t) - y(t) dt<= 1
t \in [0,1]

and that the discrete approximation y(i) converges to y(t)

I have been looking in ANDERSON-NASH Linear programming in
infinite.dimensional spaces, but they just assume that this limit
exists. Any pointers on how to prove this or some reference?

Thanks,

Diego
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