A linearly convergent algorithm for solving a class of nonconvex/affine feasibility problems

Abstract

We introduce a class of nonconvex/affine feasibility (NCF) problems that consists of finding a point in the intersection of affine constraints with a nonconvex closed set. This class captures some interesting fundamental and NP hard problems arising in various application areas such as sparse recovery of signals and affine rank minimization that we briefly review. Exploiting the special structure of NCF, we present a simple gradient projection scheme which is proven to converge to a unique solution of NCF at a linear rate under a natural assumption explicitly given defined in terms of the problem’s data.