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ounds for the original problem. The two subproblems perform the convergence test at each
iteration k.
In contrast with the new algorithrn, Dantzig's hienrchical decornposition method c m
be appiied only to staircase structures and has traditional master and subproblems. Also. it is
very difficult to apply parallel decornposition since it has to solve lower level master
probiems and subproblems serially as well as upper level master problem and subproblems.
42.3. A Strategy to use more Information from Second Level Iteration
Another strategy in utilizing more information can be defined iri order to speed up the
convergence of the algorithm. spf-' and S&J cm keep adding proposals and cuts coming
from al1 the previous first and second level iterations because they are still feasible in the
noniinking consvaints of s&' and S&.J respective1 y, no matter what cuts and proposals are
included in S@ and s
P ' , v J respectiveiy.
Thus. they cm produce nondecreasing lower bounds
and nonincreasing upper bounds at every itention of k, i and j (this is proven in section 4.4).
However. when we tned to keep al1 availabie information from the fint and second level
itentions in s&" and sP',*] . there were problems in tests.
In the next section, we define the algonthm for the case that al1 second level
information is "forgotten" every time that the fint level proceeds to another iteration;
however the algorithm that is implemented in code uses the modified strategy defined above.
4.3 The Parallel Decomposition Algorithm for the First Method
In this section. the procedure of the parallel decomposition algorithm for muiti-part
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