Constrained Quadratic Optimisation: 5.
Finishing the algorithm
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5. Finishing the
algorithm
The algorithm stops when there is no longer any valid
combination of entering and leaving basic variables that improves the objective
function. If the corresponding solution to the original problem is still not
feasible (i.e. there are still some of the additional artificial variables
introduced when setting up the super-problem that are greater than zero) then
the original problem didn’t have a feasible solution. Otherwise, the solution
to the original problem is the same as that for the super-problem. If we
introduced a change of variables at the start
of the problem because the lower limits on were not 0
then we need to unwind this change of variables, as the super-problem solution
is defined in terms of not .
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