Stochastic Programming - Index of

176 STOCHASTIC PROGRAMMING
Figure 12
Keeping or changing the candidate solutions in QDECOM.
In these cases we should decide respectively
• z 2 := x 1 , observing that no cut was added, and therefore keeping z 1
unchanged would block the procedure;
• z 3 := x 2 , realizing that x 2 is “substantially” better than z 2 —in terms of
the original objective—and that at the same time ˆF has a kink at x 2 such
that we might intuitively expect—thus clearly making use of a heuristic
argument—to make a good step forward towards the optimal kink of the
true objective;
• z 4 := z 3 , since—neither rationally nor heuristically—can we see any
convincing reason to change the candidate solution. Hence it seems
preferable to first improve the approximation of ˆF to F by introducing
the necessary optimality cuts.
After these considerations, motivating the measures to be taken in the
various steps, we want to formulate precisely one cycle of the regularized
decomposition method (RD), which with
F (x) :=c T x +
for µ ∈ (0, 1), is described as follows.
K∑
p i f i (x)
Step 1 Solve (3.6) at z k , getting x k as first-stage solution and θ k =
i=1