The problem of optimizing some given function
over the efficient set is one of the most interesting and important
concepts in multicriteria decision making. As the efficient set
is in general nonconvex, even for the case of linear
multicriteria programming problems, optimizing over the efficient
set belongs to a typical problem class of
multiextremal optimization problems, which can have local optima
different from global optima.
In this article, we consider the case where the
multicriteria programming problem is linear.
Characterizing the set of efficient solutions by
some constraint of 'reverse convex' type in the space of criteria,
we formulate the
problem of minimizing a function $f$ over the efficient
set as a global optimization problem
with a special structure.
For the resulting problem,
a decomposition branch and bound based algorithm is then
proposed, in which the branching procedure is performed in the
Convergence properties of the algorithm are
discussed, and preliminary computational results are reported.