Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
研究了欧氏空间中非凸可行性问题的投影算法，提出了局部子固非扩张性概念，结合集合在交点处的正则性条件，证明了交替投影法和Douglas-Rachford算法在非凸情形下的局部线性收敛性。
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the method of alternating projections (AP) and the Douglas--Rachford algorithm (DR). In the case of convex feasibility, firm nonexpansiveness of projection mappings is a global property that yields global convergence of AP and for consistent problems DR. A notion of local subfirm nonexpansiveness with respect to the intersection is introduced for consistent feasibility problems. This, together with a coercivity condition that relates to the regularity of the collection of sets at points in the intersection, yields local linear convergence of AP for a wide class of nonconvex problems and even local linear convergence of nonconvex instances of the DR algorithm.