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1.2 Motivation and Objectives of the Researcb
This research is motivated by Lan [1993], in which he suggested an idea of computing the
subproblems simultaneously, in a bla'k-triangular problem. by sending proposais and cuts to
immediate neighbors in his funher research. but after some reflection. it is apparent that this
scheme would probably take too many iterations for the last subproblem to hear information of
the fint subproblem. Thus, this research stmed h m the ider that all the subproblems could be
solved at the sme time using different processors in order to have benefits of parallelism. by
broadclisting dl information to ail other subprob lems for block-niangular stnicture.. It worked
well for the two-stage case. however. it failed to extend the idea of the nested decornposition to
the multi-stage case from the two-stage alsorithm due to complexity of nested algorithms.
inconsistency of weighting schemes and infeasiblilty of the solutions. The nested aigorithm didn't
fit well in paralle1 decomposition because the nested stnicture and the information aansfea lead
to m inherently seriai alprithm: it has to solve one subproblem at a time with further weighted
primal information of dl the previous subproblems on the forward ppass and with additional
weights on dual information of dl the following subproblems on the backward p as
Redizing that the linking variables and constnints cause those serious problems. we next
attempted another bruadcasting scheme by inciuding al1 linking constraints in each subpmblem
and restricting primal and dual linking variables to convex combinations of hown solutions from
other subproblerns of emlier iterations. since the nurnber of the linking variables and constraints
îce relatively smail. This ides makes it possible to apply the parallel decomposition method to the
multi-pan structure problems shown in Fi-rn 1.2.