Abstract The subject of general theory of convergence is to study, if possible, the behavior of a class of algorithms, particularly that the algorithms differ in most cases by details of implementation. This leads naturally to a general pattern in which algorithms or classes of algorithms are represented by multifunctions, i. e. the maps . An algorithm is defined by a map , which associates to each point xk already know a new point xk+1 = A(xk), . The asymptotic convergence describes how fast the sequence {xk } could arrive to an optimal solution if exists.