Generalized Gradient Methods for Solving Locally Lipschitz Feasibility Problems
Abstract
**Please note that the full text is embargoed** ABSTRACT: In this paper we study the behavior of a class of iterative
algorithms for solving feasibility problems, that is finite
systems of inequalities [see pdf for notation], where each
[see pdf for notation] is a locally Lipschitz functional on a
Hilbert space X. We show that, under quite mild conditions,
the algorithms studied in this note, if converge, then they
approximate a solution of the feasibility given problem,
provided that the feasibility problem is consistent. We prove
several convergence criteria showing that, when the envelope of
the functionals [see pdf for notation], is sufficiently
"regular", then the algorithms converge. The class of
algorithms studied in this note contains, as special cases,
many of the subgradient and projection methods of solving
convex feasibility problems discussed in the literature.