Convergence Analysis under Consistent Error Bounds

We introduce the notion of consistent error bound functions which provides a unifying framework for bounds multiple convex sets. This goes beyond classical Lipschitzian and Hölderian includes logarithmic entropic found in exponential cone. It also obtainable under theory amenable cones. Our main result is that convergence rate several projection algorithms feasibility problems can be expressed explicitly terms underlying function. Another feature usage Karamata regular variations allows us to reason about rates while bypassing certain complicated expressions. Finally, applications conic are given we show number have depending on singularity degree problem.