A Quadratically Convergent Alternating Projection Method for Nonconvex Sets

In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set x ∈ ℝn: c(x) = 0 over a possibly non-regular subset X subset ℝn. Under the constraint nondegeneracy condition, we propose a modified alternating projection method. In our proposed method, based on the concept of projective mapping for X, we alternate a Newton step for finding an inexact solution within the limiting tangent cone of X and a projection to X. Under mild conditions, we prove the local quadratic convergence of our proposed method. Preliminary numerical experiments demonstrate the high efficiency of our proposed alternating projection method.