Superiorization is envisioned as lying between the methods of optimization and of feasibility seeking. Generally speaking, optimization is a computationally more demanding task than that of finding just any feasible point. We propose that, without employing an optimization algorithm, it is possible to use certain iterative methods, designed for (the less demanding) feasibility problems, in a way that will steer the iterates toward a point that is superior, but not necessarily optimal, in a well-defined sense. The possibility to do so stems from the perturbation resilience (stability) of the feasibility seeking methods.

This is joint work with Ran Davidi and Gabor T. Herman.