Porosity-based methods for solving stochastic feasibility problems

Abstract

The notion of porosity is well known in Optimization and Nonlinear Analysis. Its importance is brought out by the fact that

the complement of a $\sigma$-porous subset of a complete pseudo-metric
space is a residual set, while the existence of the latter is essential
in many problems which apply the generic approach. Thus, under certain
circumstances, some refinements of known results can be achieved by
looking for porous sets. In 2001 Gabour, Reich and Zaslavski developed
certain generic methods for solving stochastic feasibility problems.
This topic was further investigated in 2021 by Barshad, Reich and
Zaslavski, who provided more general results in the case of unbounded
sets. In the present paper we introduce and examine new generic methods
that deal with the aforesaid problems, in which, in contrast with
previous studies, we consider sigma-porous sets instead of meager
ones.