Key points are not available for this paper at this time.
In various numerical problems one is confronted with the task of solving a system of linear inequalities: (1.1) (i = 1, … ,m) assuming, of course, that the above system is consistent. Sometimes one has, in addition, to minimize a given linear form l ( x ). Thus, in linear programming one obtains a problem of the latter type.
Shmuel Agmon (1954) studied this question.