Comparison of three approaches to studying stability of solutions to problems of discrete optimization and computational geometry

In the 1970–1980s, V. K. Leont’ev and E. N. Gordeev proposed and studied an approach to the analysis of the stability of solutions. In a number of subsequent articles, this approach was developed and the stability of solutions was analyzed on its basis. The approach itself is of a rather general nature but was originally connected with the discrete optimization problems. Later similar results, although in different terms, were published for various classes of problems. We demonstrate the proximity of approaches both on the level of statements of problems and the interpretation of results.