6bb56208f672af0dd65451f869fedfd9-Supplemental.pdf

In most applications,E " Y to begin with (ally are potential maximizer for some vector of costs, otherwise theyare not included in the set), and all points inY havepositive mass. Ittherefore also satisfies this property. We recall that we assume thatθ yields a unique maximum to the linear program onC. As a consequence, all convergent subsequences ofyn converge to the same limity pθq: it is the unique accumulation point of this sequence.Itfollowsdirectlythat yn convergesto y pθq,asitlivesinacompactset,whichyieldsthe desired result. Using different reference vectorsv yield different perturbed operations, andv " p1,2,...,dq is commonlyused.