X - UWSpace - University of Waterloo

subproblem. exchanges the information among the subproblems and tries to reach the prescribed
tolerance between the best upper bound issued by sp: and the best lower bound issued by sp:. -
Before the algonthm starts. the user selects either the lower bound subproblem, or the upper
bound subproblem, from each pan p l. ... N, while ensuring chat at least one subproblem is the
lower bound type. and at Ieast one is the upper bound type.
DO IN PARALLEL
frocessor t for t= 1, ..., N
Step O. Set k= 1, E*. and determine whether P is infeasible.
- solve spi ; if it is infeasible. send a stop signal to SP, for al1 s+t and stop. P is
infesi ble;
- if a stop signai from SP, for ail s#t is received, stop, P is infeasible;
I I
- othenvise. record optimal prima1 and dual solutions x, . y, and nt'. wll.
Step 1. Set h=k+L. exchange information, modify SP, and solve it.
- set x:" = (x:". xrl) and Y:-' = (Y:*'. y:'):
- set n:-' =(n,';-'
', rr:"
') ' and Q:-' =(RF
k-17 T, ' ,
- send (c,r:" + dry:-'), L ~~~F' for dl i. and ~,r:'l to al1 lower bound subproblems;
- send K;*'D,, O:*'L~ for al1 i, and (n:-'b, + o:'~$) to dl upper bound subproblems;
k- I
- if t is a lower bound subproblem. receive (c,r/' + dsys ), L,~:' and from SP,
for dl i and ~ t :