We review the superiorization methodology, which can be thought of, in some
cases, as lying between feasibility-seeking and constrained minimization. It is
not quite trying to solve the full fledged constrained minimization problem;
rather, the task is to find a feasible point which is superior (with respect to
an objective function value) to one returned by a feasibility-seeking only
algorithm. We distinguish between two research directions in the
superiorization methodology that nourish from the same general principle: Weak
superiorization and strong superiorization and clarify their nature.Comment: Revised version. Presented at the Tenth Workshop on Mathematical
Modelling of Environmental and Life Sciences Problems, October 16-19, 2014,
Constantza, Romania. http://www.ima.ro/workshop/tenth_workshop