A Comparison of the Forcing Function and Point-To-Set Mapping Approaches to Convergence Analysis

Abstract

A "forcing function" approach is developed for the analysis of convergence properties of "monotonic" mathematical programming algorithms. This approach differs from rather more traditional analyses based on point-to-set mappings in that it does not require point-to-set mapping concepts. A comparison is given between the forcing function and point-to-set mapping approaches that indicates that they are essentially mathematically equivalent for two major categories of algorithms, but that only the forcing function approach is readily extended to a third category of algorithms involving anti-jamming parameters.