Stochastic Programming - Index of

DYNAMIC SYSTEMS 133
S 1>1077
A A
A
S 0
>1022
S 1538 1
S
S B B B 3
0
S 0
1538.
Formally, what we are doing is as follows. We use the vocabulary of
Section 2.2. Let the random vector for stage t be given by ˜ξ t and let the
return and transition functions become r t (z t ,x t ,ξ t )andz t+1 = G t (z t ,x t ,ξ t ).
Given this, the procedure becomes
by recursively calculating
with
find f ∗ 0 (z 0 )
ft ∗ (z t )= min f t(z t ,x t )
A t(z t)≤x t≤B t(z t)
= min {ϕ
A E˜ξt t (r t (z t ,x t , ˜ξ t ),ft+1 ∗ (z t+1))}, t = T,...,0,
t(z t)≤x t≤B t(z t)
z t+1 = G t (z t ,x t ,ξ t )fort =0,...,T,
f ∗ T +1 (z T +1) =Q(z T +1 ),
where the functions satisfy the requirements of Proposition 2.2. In each stage
the problem must be solved for all possible values of the state z t . It is possible
to replace expectations (represented by E above) by other operators with
respect to ˜ξ t , such as max or min. In such a case, of course, probability
distributions are uninteresting—only the support matters.