In the paper "An algorithm for optimal partitioning of data on an interval" (link) the authors describe an algorithm for partitioning data on an interval to maximize a fitness function. The fitness function they use is the sum of the fitness of each block in the partition.
My question is, how can this be done if the fitness function were instead the minimum of the fitness of each block? More precisely, how should the algorithm be if the sum in the fitness function in equation (4) was replaced by
My guess is that the same algorithm would work, replacing equation (6) with the following:
I would think that this has been done before, but I am unable to find any references. Does anyone have a reference, or agree that my modification is correct?