  The superiorization methodology is intended to work with input data of
constrained minimization problems, i.e., a target function and a constraints
set. However, it is based on an antipodal way of thinking to the thinking that
leads constrained minimization methods. Instead of adapting unconstrained
minimization algorithms to handling constraints, it adapts feasibility-seeking
algorithms to reduce (not necessarily minimize) target function values. This is
done while retaining the feasibility-seeking nature of the algorithm and
without paying a high computational price. A guarantee that the local target
function reduction steps properly accumulate to a global target function value
reduction is still missing in spite of an ever-growing body of publications
that supply evidence of the success of the superiorization method in various
problems. We propose an analysis based on the principle of concentration of
measure that attempts to alleviate the guarantee question of the
superiorization method.
