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The superiorization methodology is intended to work with input data ofconstrained minimization problems, i.e., a target function and a constraintsset. However, it is based on an antipodal way of thinking to the thinking thatleads constrained minimization methods. Instead of adapting unconstrainedminimization algorithms to handling constraints, it adapts feasibility-seekingalgorithms to reduce (not necessarily minimize) target function values. This isdone while retaining the feasibility-seeking nature of the algorithm andwithout paying a high computational price. A guarantee that the local targetfunction reduction steps properly accumulate to a global target function valuereduction is still missing in spite of an ever-growing body of publicationsthat supply evidence of the success of the superiorization method in variousproblems. We propose an analysis based on the principle of concentration ofmeasure that attempts to alleviate the guarantee question of thesuperiorization method.

An analysis of the superiorization method via the principle of concentration of measure