Quantitative convergence analysis of iterated expansive, set-valued mappings

摘要: We develop a framework for quantitative convergence analysis of Picard iterations expansive set-valued fixed point mappings. There are two key components the analysis. The first is natural generalization single-valued averaged mappings to expansive, that characterizes type strong calmness mapping. second component this an extension well-established notion metric subregularity -- or inverse mapping at points. Convergence proved using these properties, and estimates byproduct framework. To demonstrate application theory, we prove time number results showing local linear nonconvex cyclic projections inconsistent (and consistent) feasibility problems, forward-backward algorithm structured optimization without convexity, otherwise, Douglas--Rachford minimization. This theory includes earlier approaches known results, convex nonconvex, as special cases.