diegotorquemada@yahoo.com science forum beginner
Joined: 11 Oct 2005
Posts: 17

Posted: Mon Jul 17, 2006 10:29 am Post subject:
approximating infinite linear programming problems



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 ANDERSONNASH 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 
